LMFDB - Embedded newform 189.2.u.a.67.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(4,189)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2, 12]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("189.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.u (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			67.4
Character	$\chi$	$=$	189.67
Dual form			189.2.u.a.79.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.55519 + 1.30496i) q^{2} +(1.19925 - 1.24972i) q^{3} +(0.368398 - 2.08929i) q^{4} +(0.441461 - 2.50365i) q^{5} +(-0.234236 + 3.50852i) q^{6} +(-0.472815 + 2.60316i) q^{7} +(0.123353 + 0.213653i) q^{8} +(-0.123586 - 2.99745i) q^{9} +O(q^{10})$	\(q+(-1.55519 + 1.30496i) q^{2} +(1.19925 - 1.24972i) q^{3} +(0.368398 - 2.08929i) q^{4} +(0.441461 - 2.50365i) q^{5} +(-0.234236 + 3.50852i) q^{6} +(-0.472815 + 2.60316i) q^{7} +(0.123353 + 0.213653i) q^{8} +(-0.123586 - 2.99745i) q^{9} +(2.58060 + 4.46974i) q^{10} +(-0.994702 - 5.64123i) q^{11} +(-2.16922 - 2.96598i) q^{12} +(0.494719 - 2.80569i) q^{13} +(-2.66170 - 4.66541i) q^{14} +(-2.59943 - 3.55421i) q^{15} +(3.51651 + 1.27990i) q^{16} +(2.41871 + 4.18933i) q^{17} +(4.10375 + 4.50033i) q^{18} +(-0.277852 + 0.481253i) q^{19} +(-5.06822 - 1.84468i) q^{20} +(2.68619 + 3.71273i) q^{21} +(8.90852 + 7.47513i) q^{22} +(2.10296 + 1.76459i) q^{23} +(0.414937 + 0.102068i) q^{24} +(-1.37492 - 0.500430i) q^{25} +(2.89193 + 5.00897i) q^{26} +(-3.89418 - 3.44026i) q^{27} +(5.26457 + 1.94685i) q^{28} +(0.164033 + 0.930279i) q^{29} +(8.68070 + 2.13532i) q^{30} +(0.867833 - 4.92173i) q^{31} +(-7.60271 + 2.76716i) q^{32} +(-8.24285 - 5.52217i) q^{33} +(-9.22845 - 3.35888i) q^{34} +(6.30868 + 2.33296i) q^{35} +(-6.30808 - 0.846050i) q^{36} +8.16114 q^{37} +(-0.195903 - 1.11102i) q^{38} +(-2.91303 - 3.98299i) q^{39} +(0.589368 - 0.214513i) q^{40} +(-1.92050 + 10.8917i) q^{41} +(-9.02249 - 2.26863i) q^{42} +(-4.80243 + 4.02972i) q^{43} -12.1526 q^{44} +(-7.55914 - 1.01384i) q^{45} -5.57321 q^{46} +(-0.517743 - 2.93627i) q^{47} +(5.81670 - 2.85971i) q^{48} +(-6.55289 - 2.46163i) q^{49} +(2.79130 - 1.01595i) q^{50} +(8.13612 + 2.00136i) q^{51} +(-5.67965 - 2.06722i) q^{52} +(3.07682 - 5.32920i) q^{53} +(10.5456 + 0.268508i) q^{54} -14.5628 q^{55} +(-0.614496 + 0.220088i) q^{56} +(0.268216 + 0.924380i) q^{57} +(-1.46908 - 1.23270i) q^{58} +(-8.92291 + 3.24767i) q^{59} +(-8.38341 + 4.12160i) q^{60} +(0.889765 + 5.04611i) q^{61} +(5.07300 + 8.78669i) q^{62} +(7.86129 + 1.09553i) q^{63} +(4.47042 - 7.74299i) q^{64} +(-6.80608 - 2.47721i) q^{65} +(20.0254 - 2.16855i) q^{66} +(7.29506 + 6.12129i) q^{67} +(9.64378 - 3.51005i) q^{68} +(4.72722 - 0.511912i) q^{69} +(-12.8556 + 4.60437i) q^{70} +(-5.28149 + 9.14782i) q^{71} +(0.625171 - 0.396148i) q^{72} -0.456492 q^{73} +(-12.6921 + 10.6499i) q^{74} +(-2.27427 + 1.11812i) q^{75} +(0.903117 + 0.757805i) q^{76} +(15.1553 + 0.0778908i) q^{77} +(9.72794 + 2.39292i) q^{78} +(2.52613 - 2.11967i) q^{79} +(4.75684 - 8.23909i) q^{80} +(-8.96945 + 0.740884i) q^{81} +(-11.2265 - 19.4448i) q^{82} +(0.441119 + 2.50171i) q^{83} +(8.74656 - 4.24447i) q^{84} +(11.5564 - 4.20618i) q^{85} +(2.21007 - 12.5339i) q^{86} +(1.35930 + 0.910645i) q^{87} +(1.08257 - 0.908382i) q^{88} +(3.34817 - 5.79919i) q^{89} +(13.0789 - 8.28763i) q^{90} +(7.06976 + 2.61441i) q^{91} +(4.46147 - 3.74362i) q^{92} +(-5.11001 - 6.98694i) q^{93} +(4.63689 + 3.89081i) q^{94} +(1.08223 + 0.908098i) q^{95} +(-5.65940 + 12.8198i) q^{96} +(4.52344 - 3.79562i) q^{97} +(13.4033 - 4.72295i) q^{98} +(-16.7864 + 3.67875i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9} + 3 q^{10} - 15 q^{11} - 3 q^{12} - 12 q^{13} - 30 q^{14} + 9 q^{16} + 27 q^{17} - 3 q^{18} + 3 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} - 36 q^{23} - 72 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 3 q^{30} - 3 q^{31} - 75 q^{32} + 15 q^{33} - 18 q^{34} + 15 q^{35} - 60 q^{36} - 6 q^{37} + 69 q^{38} + 51 q^{39} + 51 q^{40} - 39 q^{42} - 12 q^{43} - 6 q^{44} - 21 q^{45} - 6 q^{46} - 21 q^{47} + 90 q^{48} - 42 q^{49} - 39 q^{50} + 33 q^{51} + 9 q^{52} + 9 q^{53} - 9 q^{54} - 24 q^{55} + 111 q^{56} - 18 q^{57} - 3 q^{58} + 27 q^{59} - 63 q^{60} - 21 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} - 90 q^{65} - 3 q^{66} - 3 q^{67} - 30 q^{68} - 6 q^{69} + 39 q^{70} - 18 q^{71} + 183 q^{72} - 42 q^{73} + 51 q^{74} - 45 q^{75} - 24 q^{76} + 15 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} - 87 q^{81} - 6 q^{82} - 42 q^{83} + 135 q^{84} - 63 q^{85} - 93 q^{86} + 75 q^{87} - 51 q^{88} + 75 q^{89} - 39 q^{90} - 21 q^{91} - 66 q^{92} + 81 q^{93} + 33 q^{94} + 15 q^{95} - 171 q^{96} - 12 q^{97} - 36 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9 + 3 * q^10 - 15 * q^11 - 3 * q^12 - 12 * q^13 - 30 * q^14 + 9 * q^16 + 27 * q^17 - 3 * q^18 + 3 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 - 36 * q^23 - 72 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 3 * q^30 - 3 * q^31 - 75 * q^32 + 15 * q^33 - 18 * q^34 + 15 * q^35 - 60 * q^36 - 6 * q^37 + 69 * q^38 + 51 * q^39 + 51 * q^40 - 39 * q^42 - 12 * q^43 - 6 * q^44 - 21 * q^45 - 6 * q^46 - 21 * q^47 + 90 * q^48 - 42 * q^49 - 39 * q^50 + 33 * q^51 + 9 * q^52 + 9 * q^53 - 9 * q^54 - 24 * q^55 + 111 * q^56 - 18 * q^57 - 3 * q^58 + 27 * q^59 - 63 * q^60 - 21 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 - 90 * q^65 - 3 * q^66 - 3 * q^67 - 30 * q^68 - 6 * q^69 + 39 * q^70 - 18 * q^71 + 183 * q^72 - 42 * q^73 + 51 * q^74 - 45 * q^75 - 24 * q^76 + 15 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 - 87 * q^81 - 6 * q^82 - 42 * q^83 + 135 * q^84 - 63 * q^85 - 93 * q^86 + 75 * q^87 - 51 * q^88 + 75 * q^89 - 39 * q^90 - 21 * q^91 - 66 * q^92 + 81 * q^93 + 33 * q^94 + 15 * q^95 - 171 * q^96 - 12 * q^97 - 36 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.55519	+	1.30496i	−1.09968	+	0.922744i	−0.997404	−	0.0720117i	$-0.977058\pi$
$2$	−1.55519	+	1.30496i	−1.09968	+	0.922744i	−0.102280	+	0.994756i	$0.532614\pi$
$3$	1.19925	−	1.24972i	0.692389	−	0.721524i
$3$	1.19925	−	1.24972i	0.692389	−	0.721524i
$4$	0.368398	−	2.08929i	0.184199	−	1.04464i
$5$	0.441461	−	2.50365i	0.197427	−	1.11967i	−0.711492	−	0.702695i	$-0.751980\pi$
$5$	0.441461	−	2.50365i	0.197427	−	1.11967i	0.908919	−	0.416972i	$-0.136909\pi$
$6$	−0.234236	+	3.50852i	−0.0956263	+	1.43235i
$7$	−0.472815	+	2.60316i	−0.178707	+	0.983902i
$7$	−0.472815	+	2.60316i	−0.178707	+	0.983902i
$8$	0.123353	+	0.213653i	0.0436118	+	0.0755378i
$9$	−0.123586	−	2.99745i	−0.0411952	−	0.999151i
$10$	2.58060	+	4.46974i	0.816058	+	1.41345i
$11$	−0.994702	−	5.64123i	−0.299914	−	1.70090i	−0.646530	−	0.762889i	$-0.723780\pi$
$11$	−0.994702	−	5.64123i	−0.299914	−	1.70090i	0.346616	−	0.938007i	$-0.387331\pi$
$12$	−2.16922	−	2.96598i	−0.626200	−	0.856205i
$13$	0.494719	−	2.80569i	0.137210	−	0.778159i	−0.836084	−	0.548601i	$-0.815161\pi$
$13$	0.494719	−	2.80569i	0.137210	−	0.778159i	0.973295	−	0.229558i	$-0.0737282\pi$
$14$	−2.66170	−	4.66541i	−0.711369	−	1.24688i
$15$	−2.59943	−	3.55421i	−0.671171	−	0.917694i
$16$	3.51651	+	1.27990i	0.879127	+	0.319976i
$17$	2.41871	+	4.18933i	0.586624	+	1.01606i	0.994671	+	0.103101i	$0.0328765\pi$
$17$	2.41871	+	4.18933i	0.586624	+	1.01606i	−0.408047	+	0.912961i	$0.633790\pi$
$18$	4.10375	+	4.50033i	0.967262	+	1.06074i
$19$	−0.277852	+	0.481253i	−0.0637435	+	0.110407i	−0.896136	−	0.443780i	$-0.853637\pi$
$19$	−0.277852	+	0.481253i	−0.0637435	+	0.110407i	0.832392	+	0.554187i	$0.186971\pi$
$20$	−5.06822	−	1.84468i	−1.13329	−	0.412483i
$21$	2.68619	+	3.71273i	0.586175	+	0.810185i
$22$	8.90852	+	7.47513i	1.89930	+	1.59370i
$23$	2.10296	+	1.76459i	0.438497	+	0.367943i	0.835147	−	0.550027i	$-0.185383\pi$
$23$	2.10296	+	1.76459i	0.438497	+	0.367943i	−0.396649	+	0.917970i	$0.629827\pi$
$24$	0.414937	+	0.102068i	0.0846987	+	0.0208346i
$25$	−1.37492	−	0.500430i	−0.274984	−	0.100086i
$26$	2.89193	+	5.00897i	0.567154	+	0.982339i
$27$	−3.89418	−	3.44026i	−0.749435	−	0.662078i
$28$	5.26457	+	1.94685i	0.994911	+	0.367920i
$29$	0.164033	+	0.930279i	0.0304602	+	0.172749i	0.996243	−	0.0866047i	$-0.0276017\pi$
$29$	0.164033	+	0.930279i	0.0304602	+	0.172749i	−0.965783	+	0.259353i	$0.916491\pi$
$30$	8.68070	+	2.13532i	1.58487	+	0.389854i
$31$	0.867833	−	4.92173i	0.155867	−	0.883968i	−0.802121	−	0.597161i	$-0.796295\pi$
$31$	0.867833	−	4.92173i	0.155867	−	0.883968i	0.957989	−	0.286807i	$-0.0925937\pi$
$32$	−7.60271	+	2.76716i	−1.34398	+	0.489169i
$33$	−8.24285	−	5.52217i	−1.43490	−	0.961286i
$34$	−9.22845	−	3.35888i	−1.58267	−	0.576043i
$35$	6.30868	+	2.33296i	1.06636	+	0.394342i
$36$	−6.30808	−	0.846050i	−1.05135	−	0.141008i
$37$	8.16114			1.34168			0.670841	−	0.741601i	$-0.265933\pi$
$37$	8.16114			1.34168			0.670841	+	0.741601i	$0.265933\pi$
$38$	−0.195903	−	1.11102i	−0.0317797	−	0.180232i
$39$	−2.91303	−	3.98299i	−0.466458	−	0.637790i
$40$	0.589368	−	0.214513i	0.0931873	−	0.0339174i
$41$	−1.92050	+	10.8917i	−0.299932	+	1.70100i	0.346520	+	0.938043i	$0.387363\pi$
$41$	−1.92050	+	10.8917i	−0.299932	+	1.70100i	−0.646452	+	0.762955i	$0.723748\pi$
$42$	−9.02249	−	2.26863i	−1.39220	−	0.350058i
$43$	−4.80243	+	4.02972i	−0.732364	+	0.614526i	−0.930775	−	0.365593i	$-0.880866\pi$
$43$	−4.80243	+	4.02972i	−0.732364	+	0.614526i	0.198411	+	0.980119i	$0.436422\pi$
$44$	−12.1526			−1.83208
$45$	−7.55914	−	1.01384i	−1.12685	−	0.151135i
$46$	−5.57321			−0.821725
$47$	−0.517743	−	2.93627i	−0.0755206	−	0.428299i	−0.999002	−	0.0446563i	$-0.985781\pi$
$47$	−0.517743	−	2.93627i	−0.0755206	−	0.428299i	0.923482	−	0.383642i	$-0.125330\pi$
$48$	5.81670	−	2.85971i	0.839569	−	0.412764i
$49$	−6.55289	−	2.46163i	−0.936127	−	0.351661i
$50$	2.79130	−	1.01595i	0.394749	−	0.143677i
$51$	8.13612	+	2.00136i	1.13929	+	0.280247i
$52$	−5.67965	−	2.06722i	−0.787626	−	0.286672i
$53$	3.07682	−	5.32920i	0.422633	−	0.732022i	−0.573563	−	0.819162i	$-0.694439\pi$
$53$	3.07682	−	5.32920i	0.422633	−	0.732022i	0.996196	+	0.0871392i	$0.0277725\pi$
$54$	10.5456	+	0.268508i	1.43507	+	0.0365393i
$55$	−14.5628			−1.96365
$56$	−0.614496	+	0.220088i	−0.0821155	+	0.0294106i
$57$	0.268216	+	0.924380i	0.0355261	+	0.122437i
$58$	−1.46908	−	1.23270i	−0.192899	−	0.161862i
$59$	−8.92291	+	3.24767i	−1.16166	+	0.422811i	−0.849691	−	0.527280i	$-0.823212\pi$
$59$	−8.92291	+	3.24767i	−1.16166	+	0.422811i	−0.311972	+	0.950091i	$0.600990\pi$
$60$	−8.38341	+	4.12160i	−1.08229	+	0.532097i
$61$	0.889765	+	5.04611i	0.113923	+	0.646088i	0.987278	+	0.159004i	$0.0508283\pi$
$61$	0.889765	+	5.04611i	0.113923	+	0.646088i	−0.873355	+	0.487084i	$0.838061\pi$
$62$	5.07300	+	8.78669i	0.644271	+	1.11591i
$63$	7.86129	+	1.09553i	0.990429	+	0.138024i
$64$	4.47042	−	7.74299i	0.558802	−	0.967874i
$65$	−6.80608	−	2.47721i	−0.844190	−	0.307260i
$66$	20.0254	−	2.16855i	2.46495	−	0.266930i
$67$	7.29506	+	6.12129i	0.891234	+	0.747834i	0.968457	−	0.249180i	$-0.0801610\pi$
$67$	7.29506	+	6.12129i	0.891234	+	0.747834i	−0.0772232	+	0.997014i	$0.524605\pi$
$68$	9.64378	−	3.51005i	1.16948	−	0.425656i
$69$	4.72722	−	0.511912i	0.569090	−	0.0616269i
$70$	−12.8556	+	4.60437i	−1.53654	+	0.550327i
$71$	−5.28149	+	9.14782i	−0.626798	+	1.08565i	0.361392	+	0.932414i	$0.382302\pi$
$71$	−5.28149	+	9.14782i	−0.626798	+	1.08565i	−0.988190	+	0.153232i	$0.951032\pi$
$72$	0.625171	−	0.396148i	0.0736771	−	0.0466865i
$73$	−0.456492			−0.0534283			−0.0267141	−	0.999643i	$-0.508504\pi$
$73$	−0.456492			−0.0534283			−0.0267141	+	0.999643i	$0.508504\pi$
$74$	−12.6921	+	10.6499i	−1.47543	+	1.23803i
$75$	−2.27427	+	1.11812i	−0.262610	+	0.129109i
$76$	0.903117	+	0.757805i	0.103595	+	0.0869262i
$77$	15.1553	+	0.0778908i	1.72711	+	0.00887648i
$78$	9.72794	+	2.39292i	1.10147	+	0.270945i
$79$	2.52613	−	2.11967i	0.284212	−	0.238482i	−0.489525	−	0.871989i	$-0.662830\pi$
$79$	2.52613	−	2.11967i	0.284212	−	0.238482i	0.773737	+	0.633507i	$0.218385\pi$
$80$	4.75684	−	8.23909i	0.531831	−	0.921158i
$81$	−8.96945	+	0.740884i	−0.996606	+	0.0823204i
$82$	−11.2265	−	19.4448i	−1.23976	−	2.14732i
$83$	0.441119	+	2.50171i	0.0484190	+	0.274598i	0.999399	−	0.0346532i	$-0.0110327\pi$
$83$	0.441119	+	2.50171i	0.0484190	+	0.274598i	−0.950980	+	0.309251i	$0.899922\pi$
$84$	8.74656	−	4.24447i	0.954328	−	0.463109i
$85$	11.5564	−	4.20618i	1.25347	−	0.456225i
$86$	2.21007	−	12.5339i	0.238318	−	1.35157i
$87$	1.35930	+	0.910645i	0.145733	+	0.0976314i
$88$	1.08257	−	0.908382i	0.115402	−	0.0968339i
$89$	3.34817	−	5.79919i	0.354905	−	0.614713i	−0.632197	−	0.774808i	$-0.717847\pi$
$89$	3.34817	−	5.79919i	0.354905	−	0.614713i	0.987102	+	0.160095i	$0.0511799\pi$
$90$	13.0789	−	8.28763i	1.37864	−	0.873593i
$91$	7.06976	+	2.61441i	0.741112	+	0.274064i
$92$	4.46147	−	3.74362i	0.465140	−	0.390299i
$93$	−5.11001	−	6.98694i	−0.529884	−	0.724512i
$94$	4.63689	+	3.89081i	0.478259	+	0.401307i
$95$	1.08223	+	0.908098i	0.111034	+	0.0931689i
$96$	−5.65940	+	12.8198i	−0.577610	+	1.30841i
$97$	4.52344	−	3.79562i	0.459286	−	0.385387i	−0.383582	−	0.923507i	$-0.625310\pi$
$97$	4.52344	−	3.79562i	0.459286	−	0.385387i	0.842868	+	0.538120i	$0.180865\pi$
$98$	13.4033	−	4.72295i	1.35394	−	0.477090i
$99$	−16.7864	+	3.67875i	−1.68710	+	0.369728i
$100$	−1.55206	+	2.68825i	−0.155206	+	0.268825i
$101$	2.38567	−	2.00182i	0.237383	−	0.199188i	−0.516334	−	0.856388i	$-0.672704\pi$
$101$	2.38567	−	2.00182i	0.237383	−	0.199188i	0.753717	+	0.657199i	$0.228259\pi$
$102$	−15.2649	+	7.50480i	−1.51145	+	0.743086i
$103$	−2.15981	+	12.2489i	−0.212812	+	1.20692i	0.671850	+	0.740687i	$0.265500\pi$
$103$	−2.15981	+	12.2489i	−0.212812	+	1.20692i	−0.884663	+	0.466232i	$0.845611\pi$
$104$	0.660470	−	0.240391i	0.0647644	−	0.0235723i
$105$	10.4812	−	5.08626i	1.02286	−	0.496368i
$106$	2.16936	+	12.3030i	0.210706	+	1.19498i
$107$	3.72902	+	6.45885i	0.360498	+	0.624401i	0.988043	−	0.154180i	$-0.0492734\pi$
$107$	3.72902	+	6.45885i	0.360498	+	0.624401i	−0.627545	+	0.778580i	$0.715940\pi$
$108$	−8.62230	+	6.86868i	−0.829682	+	0.660939i
$109$	7.64451	−	13.2407i	0.732211	−	1.26823i	−0.223726	−	0.974652i	$-0.571822\pi$
$109$	7.64451	−	13.2407i	0.732211	−	1.26823i	0.955936	−	0.293574i	$-0.0948447\pi$
$110$	22.6479	−	19.0038i	2.15939	−	1.81194i
$111$	9.78727	−	10.1991i	0.928966	−	0.968057i
$112$	−4.99446	+	8.54888i	−0.471932	+	0.807793i
$113$	13.2747	+	11.1388i	1.24878	+	1.04785i	0.996785	+	0.0801258i	$0.0255322\pi$
$113$	13.2747	+	11.1388i	1.24878	+	1.04785i	0.251998	+	0.967728i	$0.418912\pi$
$114$	−1.62340	−	1.08757i	−0.152046	−	0.101861i
$115$	5.34630	−	4.48608i	0.498545	−	0.418329i
$116$	2.00405			0.186072
$117$	−8.47107	−	1.13616i	−0.783151	−	0.105038i
$118$	9.63872	−	16.6948i	0.887316	−	1.53688i
$119$	−12.0491	+	4.31552i	−1.10454	+	0.395603i
$120$	0.438722	−	0.993798i	0.0400496	−	0.0907210i
$121$	−20.4975	+	7.46047i	−1.86341	+	0.678224i
$122$	−7.96871	−	6.68654i	−0.721453	−	0.605371i
$123$	11.3084	+	15.4620i	1.01964	+	1.39416i
$124$	−9.96320	−	3.62631i	−0.894722	−	0.325652i
$125$	4.49581	−	7.78697i	0.402117	−	0.696488i
$126$	−13.6554	+	8.55489i	−1.21652	+	0.762130i
$127$	2.09524	+	3.62907i	0.185923	+	0.322027i	0.943887	−	0.330268i	$-0.107139\pi$
$127$	2.09524	+	3.62907i	0.185923	+	0.322027i	−0.757964	+	0.652296i	$0.773806\pi$
$128$	0.342087	+	1.94007i	0.0302365	+	0.171480i
$129$	−0.723321	+	10.8343i	−0.0636849	+	0.953910i
$130$	13.8174	−	5.02911i	1.21186	−	0.441083i
$131$	−2.06049	−	1.72895i	−0.180026	−	0.151059i	0.548322	−	0.836267i	$-0.315267\pi$
$131$	−2.06049	−	1.72895i	−0.180026	−	0.151059i	−0.728347	+	0.685208i	$0.759711\pi$
$132$	−14.5741	+	15.1873i	−1.26851	+	1.32189i
$133$	−1.12141	−	0.950836i	−0.0972383	−	0.0824479i
$134$	−19.3332			−1.67013
$135$	−10.3323	+	8.23093i	−0.889266	+	0.708405i
$136$	−0.596709	+	1.03353i	−0.0511674	+	0.0886245i
$137$	−2.15297	−	0.783616i	−0.183940	−	0.0669489i	0.248408	−	0.968656i	$-0.420093\pi$
$137$	−2.15297	−	0.783616i	−0.183940	−	0.0669489i	−0.432348	+	0.901707i	$0.642315\pi$
$138$	−6.68369	+	6.96494i	−0.568953	+	0.592895i
$139$	2.00556	−	0.729963i	0.170109	−	0.0619147i	−0.255562	−	0.966793i	$-0.582260\pi$
$139$	2.00556	−	0.729963i	0.170109	−	0.0619147i	0.425671	+	0.904878i	$0.360038\pi$
$140$	7.19833	−	12.3212i	0.608370	−	1.04133i
$141$	−4.29041	−	2.87429i	−0.361317	−	0.242059i
$142$	−3.72380	−	21.1187i	−0.312494	−	1.77224i
$143$	−16.3197			−1.36472
$144$	3.40187	−	10.6988i	0.283489	−	0.891563i
$145$	2.40151			0.199435
$146$	0.709930	−	0.595702i	0.0587542	−	0.0493006i
$147$	−10.9349	+	5.23715i	−0.901896	+	0.431953i
$148$	3.00655	−	17.0510i	0.247137	−	1.40158i
$149$	7.63172	−	2.77772i	0.625215	−	0.227560i	−0.00993237	−	0.999951i	$-0.503162\pi$
$149$	7.63172	−	2.77772i	0.625215	−	0.227560i	0.635147	+	0.772391i	$0.280939\pi$
$150$	2.07782	−	4.70671i	0.169653	−	0.384301i
$151$	−2.79284	−	15.8390i	−0.227278	−	1.28896i	−0.858283	−	0.513177i	$-0.828468\pi$
$151$	−2.79284	−	15.8390i	−0.227278	−	1.28896i	0.631005	−	0.775779i	$-0.282643\pi$
$152$	−0.137095			−0.0111199
$153$	12.2584	−	7.76771i	0.991033	−	0.627983i
$154$	−23.6711	+	19.6559i	−1.90747	+	1.58392i
$155$	−11.9392	−	4.34550i	−0.958977	−	0.349039i
$156$	−9.39478	+	4.61883i	−0.752185	+	0.369803i
$157$	−5.28662	+	1.92417i	−0.421918	+	0.153566i	−0.544249	−	0.838924i	$-0.683185\pi$
$157$	−5.28662	+	1.92417i	−0.421918	+	0.153566i	0.122331	+	0.992489i	$0.460963\pi$
$158$	−1.16252	+	6.59298i	−0.0924851	+	0.524509i
$159$	−2.97012	−	10.2362i	−0.235545	−	0.811785i
$160$	3.57170	+	20.2561i	0.282368	+	1.60139i
$161$	−5.58783	+	4.64001i	−0.440382	+	0.365684i
$162$	12.9824	−	12.8570i	1.01999	−	1.01014i
$163$	−0.362739	−	0.628282i	−0.0284119	−	0.0492108i	0.851470	−	0.524404i	$-0.175712\pi$
$163$	−0.362739	−	0.628282i	−0.0284119	−	0.0492108i	−0.879882	+	0.475193i	$0.842378\pi$
$164$	22.0484	+	8.02496i	1.72169	+	0.626644i
$165$	−17.4645	+	18.1994i	−1.35961	+	1.41682i
$166$	−3.95064	−	3.31498i	−0.306629	−	0.257293i
$167$	−4.91108	−	4.12088i	−0.380030	−	0.318883i	0.432684	−	0.901546i	$-0.357567\pi$
$167$	−4.91108	−	4.12088i	−0.380030	−	0.318883i	−0.812714	+	0.582662i	$0.802011\pi$
$168$	−0.461888	+	1.03189i	−0.0356354	+	0.0796119i
$169$	4.58884	+	1.67020i	0.352988	+	0.128477i
$170$	−12.4835	+	21.6220i	−0.957438	+	1.65833i
$171$	1.47687	+	0.773371i	0.112939	+	0.0591412i
$172$	6.65004	+	11.5182i	0.507061	+	0.878256i
$173$	16.9804	+	6.18036i	1.29100	+	0.469884i	0.894054	−	0.447959i	$-0.147849\pi$
$173$	16.9804	+	6.18036i	1.29100	+	0.469884i	0.396942	+	0.917844i	$0.370071\pi$
$174$	−3.30232	+	0.357609i	−0.250349	+	0.0271103i
$175$	1.95278	−	3.34253i	0.147616	−	0.252671i
$176$	3.72236	−	21.1106i	0.280584	−	1.59127i
$177$	−6.64215	+	15.0459i	−0.499255	+	1.13092i
$178$	2.36067	+	13.3880i	0.176940	+	1.00348i
$179$	6.06566	+	10.5060i	0.453369	+	0.785257i	0.998593	−	0.0530329i	$-0.0168888\pi$
$179$	6.06566	+	10.5060i	0.453369	+	0.785257i	−0.545224	+	0.838290i	$0.683555\pi$
$180$	−4.90299	+	15.4197i	−0.365447	+	1.14932i
$181$	−1.82583	−	3.16242i	−0.135713	−	0.235061i	0.790157	−	0.612905i	$-0.209999\pi$
$181$	−1.82583	−	3.16242i	−0.135713	−	0.235061i	−0.925869	+	0.377844i	$0.876666\pi$
$182$	−14.4065	+	5.15984i	−1.06788	+	0.382473i
$183$	7.37326	+	4.93960i	0.545047	+	0.365146i
$184$	−0.117605	+	0.666971i	−0.00866995	+	0.0491697i
$185$	3.60283	−	20.4326i	0.264885	−	1.50224i
$186$	17.0647	+	4.19765i	1.25124	+	0.307787i
$187$	21.2271	−	17.8117i	1.55228	−	1.30252i
$188$	−6.32545			−0.461331
$189$	10.7968	−	8.51057i	0.785349	−	0.619053i
$190$	−2.86810			−0.208074
$191$	−1.26218	+	1.05909i	−0.0913281	+	0.0766334i	−0.687309	−	0.726366i	$-0.741208\pi$
$191$	−1.26218	+	1.05909i	−0.0913281	+	0.0766334i	0.595981	+	0.802999i	$0.296764\pi$
$192$	−4.31539	−	14.8726i	−0.311436	−	1.07333i
$193$	−1.30894	+	7.42335i	−0.0942194	+	0.534345i	0.900764	+	0.434308i	$0.143007\pi$
$193$	−1.30894	+	7.42335i	−0.0942194	+	0.534345i	−0.994984	+	0.100037i	$0.968104\pi$
$194$	−2.08168	+	11.8058i	−0.149456	+	0.847607i
$195$	−11.2580	+	5.53487i	−0.806204	+	0.396360i
$196$	−7.55712	+	12.7840i	−0.539795	+	0.913145i
$197$	−3.93907	−	6.82267i	−0.280647	−	0.486095i	0.690897	−	0.722953i	$-0.257216\pi$
$197$	−3.93907	−	6.82267i	−0.280647	−	0.486095i	−0.971544	+	0.236858i	$0.923882\pi$
$198$	21.3054	−	27.6267i	1.51411	−	1.96334i
$199$	−0.493723	−	0.855154i	−0.0349991	−	0.0606202i	0.847995	−	0.530004i	$-0.177810\pi$
$199$	−0.493723	−	0.855154i	−0.0349991	−	0.0606202i	−0.882994	+	0.469384i	$0.844476\pi$
$200$	−0.0626816	−	0.355485i	−0.00443226	−	0.0251366i
$201$	16.3985	−	1.77580i	1.15666	−	0.125255i
$202$	−1.09788	+	6.22640i	−0.0772467	+	0.438088i
$203$	−2.49922	−	0.0128447i	−0.175411	−	0.000901525i
$204$	7.17876	−	16.2614i	0.502614	−	1.13853i
$205$	26.4212	+	9.61653i	1.84534	+	0.671647i
$206$	−12.6254	−	21.8678i	−0.879651	−	1.52360i
$207$	5.02939	−	6.52160i	0.349566	−	0.453282i
$208$	5.33071	−	9.23305i	0.369618	−	0.640197i
$209$	2.99124	+	1.08872i	0.206908	+	0.0753085i
$210$	−9.66294	+	21.5876i	−0.666806	+	1.48969i
$211$	−12.2920	−	10.3142i	−0.846215	−	0.710059i	0.112738	−	0.993625i	$-0.464038\pi$
$211$	−12.2920	−	10.3142i	−0.846215	−	0.710059i	−0.958953	+	0.283566i	$0.908482\pi$
$212$	−10.0008	−	8.39163i	−0.686855	−	0.576340i
$213$	5.09834	+	17.5709i	0.349332	+	1.20394i
$214$	−14.2279	−	5.17851i	−0.972596	−	0.353996i
$215$	7.96892	+	13.8026i	0.543476	+	0.941328i
$216$	0.254664	−	1.25637i	0.0173277	−	0.0854850i
$217$	12.4017	+	4.58617i	0.841883	+	0.311330i
$218$	5.38987	+	30.5675i	0.365048	+	2.07029i
$219$	−0.547449	+	0.570485i	−0.0369932	+	0.0385498i
$220$	−5.36491	+	30.4259i	−0.361702	+	2.05132i
$221$	12.9506	−	4.71362i	0.871149	−	0.317072i
$222$	−1.91163	+	28.6335i	−0.128300	+	1.92175i
$223$	5.45194	+	1.98434i	0.365089	+	0.132881i	0.518049	−	0.855351i	$-0.326658\pi$
$223$	5.45194	+	1.98434i	0.365089	+	0.132881i	−0.152960	+	0.988232i	$0.548881\pi$
$224$	−3.60869	−	21.0994i	−0.241116	−	1.40976i
$225$	−1.33009	+	4.18310i	−0.0886730	+	0.278874i
$226$	−35.1804			−2.34017
$227$	−4.38402	−	24.8630i	−0.290978	−	1.65022i	−0.683115	−	0.730310i	$-0.739375\pi$
$227$	−4.38402	−	24.8630i	−0.290978	−	1.65022i	0.392138	−	0.919907i	$-0.371736\pi$
$228$	2.03011	−	0.219841i	0.134447	−	0.0145593i
$229$	−19.3442	+	7.04070i	−1.27830	+	0.465263i	−0.889869	−	0.456216i	$-0.849205\pi$
$229$	−19.3442	+	7.04070i	−1.27830	+	0.465263i	−0.388429	+	0.921478i	$0.626982\pi$
$230$	−2.46036	+	13.9534i	−0.162231	+	0.920058i
$231$	18.2724	−	18.8465i	1.20224	−	1.24001i
$232$	−0.178523	+	0.149799i	−0.0117206	+	0.00983476i
$233$	28.9197			1.89460			0.947298	−	0.320355i	$-0.103802\pi$
$233$	28.9197			1.89460			0.947298	+	0.320355i	$0.103802\pi$
$234$	14.6567	−	9.28745i	0.958141	−	0.607140i
$235$	−7.57995			−0.494462
$236$	3.49815	+	19.8390i	0.227710	+	1.29141i
$237$	0.380474	−	5.69897i	0.0247145	−	0.370188i
$238$	13.1071	−	22.4350i	0.849604	−	1.45425i
$239$	−13.0309	+	4.74288i	−0.842902	+	0.306791i	−0.727143	−	0.686486i	$-0.759152\pi$
$239$	−13.0309	+	4.74288i	−0.842902	+	0.306791i	−0.115759	+	0.993277i	$0.536930\pi$
$240$	−4.59187	−	15.8255i	−0.296404	−	1.02153i
$241$	−7.61509	−	2.77167i	−0.490531	−	0.178539i	0.0848993	−	0.996390i	$-0.472943\pi$
$241$	−7.61509	−	2.77167i	−0.490531	−	0.178539i	−0.575430	+	0.817851i	$0.695165\pi$
$242$	22.1418	−	38.3507i	1.42333	−	2.46528i
$243$	−9.83075	+	12.0978i	−0.630643	+	0.776073i
$244$	10.8706			0.695917
$245$	−9.05590	+	15.3194i	−0.578560	+	0.978723i
$246$	−37.7639	−	9.28933i	−2.40774	−	0.592266i
$247$	1.21279	+	1.01765i	0.0771680	+	0.0647516i
$248$	1.15859	−	0.421693i	0.0735706	−	0.0267775i
$249$	3.65544	+	2.44891i	0.231654	+	0.155193i
$250$	3.16984	+	17.9770i	0.200478	+	1.13697i
$251$	1.46517	+	2.53775i	0.0924809	+	0.160182i	0.908554	−	0.417766i	$-0.137187\pi$
$251$	1.46517	+	2.53775i	0.0924809	+	0.160182i	−0.816074	+	0.577948i	$0.803854\pi$
$252$	5.18496	−	16.0209i	0.326622	−	1.00922i
$253$	7.86266	−	13.6185i	0.494321	−	0.856189i
$254$	−7.99427	−	2.90968i	−0.501605	−	0.182569i
$255$	8.60250	−	19.4865i	0.538709	−	1.22029i
$256$	10.6344	+	8.92335i	0.664652	+	0.557709i
$257$	−16.2975	+	5.93181i	−1.01661	+	0.370016i	−0.795968	−	0.605339i	$-0.793038\pi$
$257$	−16.2975	+	5.93181i	−1.01661	+	0.370016i	−0.220643	+	0.975355i	$0.570816\pi$
$258$	−13.0134	−	17.7933i	−0.810181	−	1.10776i
$259$	−3.85871	+	21.2448i	−0.239768	+	1.32008i
$260$	−7.68296	+	13.3073i	−0.476477	+	0.825282i
$261$	2.76820	−	0.606651i	0.171347	−	0.0375508i
$262$	5.46065			0.337360
$263$	−11.2893	+	9.47281i	−0.696125	+	0.584119i	−0.920668	−	0.390346i	$-0.872356\pi$
$263$	−11.2893	+	9.47281i	−0.696125	+	0.584119i	0.224543	+	0.974464i	$0.427911\pi$
$264$	0.163052	−	2.44228i	0.0100351	−	0.150312i
$265$	−11.9842	−	10.0559i	−0.736182	−	0.617730i
$266$	2.98480	+	0.0153404i	0.183010	+	0.000940577i
$267$	−3.23205	−	11.1390i	−0.197798	−	0.681693i
$268$	15.4766	−	12.9864i	0.945386	−	0.793273i
$269$	−15.0329	+	26.0378i	−0.916573	+	1.58755i	−0.111992	+	0.993709i	$0.535723\pi$
$269$	−15.0329	+	26.0378i	−0.916573	+	1.58755i	−0.804582	+	0.593842i	$0.797610\pi$
$270$	5.32771	−	26.2839i	0.324234	−	1.59959i
$271$	−9.41096	−	16.3003i	−0.571675	−	0.990170i	−0.996394	−	0.0848450i	$-0.972960\pi$
$271$	−9.41096	−	16.3003i	−0.571675	−	0.990170i	0.424719	−	0.905325i	$-0.360373\pi$
$272$	3.14348	+	17.8275i	0.190601	+	1.08095i
$273$	11.7457	−	5.69986i	0.710882	−	0.344971i
$274$	4.37085	−	1.59086i	0.264053	−	0.0961074i
$275$	−1.45541	+	8.25402i	−0.0877643	+	0.497736i
$276$	0.671967	−	10.0651i	0.0404477	−	0.605849i
$277$	23.2185	−	19.4826i	1.39506	−	1.17060i	0.431821	−	0.901959i	$-0.357871\pi$
$277$	23.2185	−	19.4826i	1.39506	−	1.17060i	0.963242	−	0.268637i	$-0.0865732\pi$
$278$	−2.16645	+	3.75240i	−0.129935	+	0.225054i
$279$	−14.8599	−	1.99303i	−0.889639	−	0.119320i
$280$	0.279748	+	1.63565i	0.0167182	+	0.0977485i
$281$	−3.64722	+	3.06038i	−0.217575	+	0.182567i	−0.745060	−	0.666997i	$-0.767579\pi$
$281$	−3.64722	+	3.06038i	−0.217575	+	0.182567i	0.527486	+	0.849564i	$0.323135\pi$
$282$	10.4232	−	1.12873i	0.620694	−	0.0672150i
$283$	−7.53211	−	6.32019i	−0.447738	−	0.375696i	0.390858	−	0.920451i	$-0.372178\pi$
$283$	−7.53211	−	6.32019i	−0.447738	−	0.375696i	−0.838596	+	0.544755i	$0.816623\pi$
$284$	17.1667	+	14.4046i	1.01866	+	0.854756i
$285$	2.43273	−	0.263441i	0.144103	−	0.0156049i
$286$	25.3801	−	21.2965i	1.50076	−	1.25929i
$287$	−27.4448	−	10.1491i	−1.62002	−	0.599084i
$288$	9.23401	+	22.4468i	0.544120	+	1.32269i
$289$	−3.20033	+	5.54313i	−0.188255	+	0.326067i
$290$	−3.73480	+	3.13387i	−0.219315	+	0.184027i
$291$	0.681301	−	10.2049i	0.0399386	−	0.598224i
$292$	−0.168171	+	0.953743i	−0.00984144	+	0.0558136i
$293$	−19.5850	+	7.12836i	−1.14417	+	0.416443i	−0.843417	−	0.537260i	$-0.819460\pi$
$293$	−19.5850	+	7.12836i	−1.14417	+	0.416443i	−0.300751	+	0.953703i	$0.597237\pi$
$294$	10.1716	−	22.4143i	0.593219	−	1.30723i
$295$	4.19192	+	23.7736i	0.244063	+	1.38415i
$296$	1.00670	+	1.74365i	0.0585131	+	0.101348i
$297$	−15.5337	+	25.3900i	−0.901360	+	1.47328i
$298$	−8.24395	+	14.2789i	−0.477559	+	0.827157i
$299$	5.99128	−	5.02728i	0.346484	−	0.290735i
$300$	1.49824	+	5.16353i	0.0865007	+	0.298116i
$301$	−8.21934	−	14.4068i	−0.473755	−	0.830395i
$302$	25.0125	+	20.9880i	1.43931	+	1.20772i
$303$	0.359319	−	5.38210i	0.0206424	−	0.309193i
$304$	−1.59303	+	1.33671i	−0.0913663	+	0.0766654i
$305$	13.0265			0.745895
$306$	−8.92758	+	28.0769i	−0.510356	+	1.60505i
$307$	−16.2647	+	28.1714i	−0.928278	+	1.60782i	−0.142075	+	0.989856i	$0.545377\pi$
$307$	−16.2647	+	28.1714i	−0.928278	+	1.60782i	−0.786203	+	0.617968i	$0.787956\pi$
$308$	5.74594	−	31.6352i	0.327405	−	1.80258i
$309$	12.7175	+	17.3887i	0.723472	+	0.989206i
$310$	24.2383	−	8.82203i	1.37665	−	0.501058i
$311$	−4.85696	−	4.07547i	−0.275413	−	0.231099i	0.494610	−	0.869115i	$-0.335311\pi$
$311$	−4.85696	−	4.07547i	−0.275413	−	0.231099i	−0.770023	+	0.638016i	$0.779755\pi$
$312$	0.491649	−	1.11369i	0.0278342	−	0.0630503i
$313$	−25.5353	−	9.29409i	−1.44334	−	0.525333i	−0.502617	−	0.864509i	$-0.667630\pi$
$313$	−25.5353	−	9.29409i	−1.44334	−	0.525333i	−0.940723	+	0.339176i	$0.889852\pi$
$314$	5.71072	−	9.89125i	0.322274	−	0.558196i
$315$	6.21327	−	19.1983i	0.350078	−	1.08170i
$316$	−3.49799	−	6.05870i	−0.196777	−	0.340828i
$317$	−0.676743	−	3.83800i	−0.0380097	−	0.215564i	0.959887	−	0.280387i	$-0.0904628\pi$
$317$	−0.676743	−	3.83800i	−0.0380097	−	0.215564i	−0.997897	+	0.0648232i	$0.979352\pi$
$318$	17.9769	+	12.0434i	1.00809	+	0.675358i
$319$	5.08476	−	1.85070i	0.284692	−	0.103619i
$320$	−17.4122	−	14.6106i	−0.973373	−	0.816757i
$321$	12.5438	+	3.08558i	0.700125	+	0.172220i
$322$	2.63510	−	14.5080i	0.146848	−	0.808497i
$323$	−2.68817			−0.149574
$324$	−1.75641	+	19.0127i	−0.0975783	+	1.05626i
$325$	−2.08425	+	3.61003i	−0.115613	+	0.200248i
$326$	1.38401	+	0.503737i	0.0766531	+	0.0278994i
$327$	−7.37940	−	25.4324i	−0.408082	−	1.40641i
$328$	−2.56394	+	0.933199i	−0.141570	+	0.0515273i
$329$	7.88837	+	0.0405422i	0.434900	+	0.00223517i
$330$	3.41113	−	51.0939i	0.187776	−	2.81262i
$331$	4.84703	+	27.4889i	0.266417	+	1.51092i	0.764971	+	0.644065i	$0.222754\pi$
$331$	4.84703	+	27.4889i	0.266417	+	1.51092i	−0.498554	+	0.866859i	$0.666135\pi$
$332$	5.38930			0.295776
$333$	−1.00860	−	24.4626i	−0.0552709	−	1.34054i
$334$	13.0152			0.712161
$335$	18.5461	−	15.5620i	1.01328	−	0.850242i
$336$	4.69407	+	16.4939i	0.256082	+	0.899818i
$337$	−0.429872	+	2.43793i	−0.0234166	+	0.132802i	−0.994275	−	0.106852i	$-0.965923\pi$
$337$	−0.429872	+	2.43793i	−0.0234166	+	0.132802i	0.970858	+	0.239654i	$0.0770341\pi$
$338$	−9.31604	+	3.39076i	−0.506726	+	0.184433i
$339$	29.8402	−	3.23140i	1.62070	−	0.175505i
$340$	−4.53058	−	25.6942i	−0.245705	−	1.39346i
$341$	−28.6278			−1.55028
$342$	−3.30603	+	0.724518i	−0.178770	+	0.0391774i
$343$	9.50631	−	15.8943i	0.513293	−	0.858214i
$344$	−1.45335	−	0.528978i	−0.0783596	−	0.0285206i
$345$	0.805236	−	12.0613i	0.0433525	−	0.649358i
$346$	−34.4728	+	12.5471i	−1.85327	+	0.674535i
$347$	−3.76942	+	21.3774i	−0.202353	+	1.14760i	0.699198	+	0.714928i	$0.253541\pi$
$347$	−3.76942	+	21.3774i	−0.202353	+	1.14760i	−0.901551	+	0.432673i	$0.857571\pi$
$348$	2.40337	−	2.50450i	0.128834	−	0.134255i
$349$	−2.32120	−	13.1642i	−0.124251	−	0.704661i	−0.981750	−	0.190176i	$-0.939094\pi$
$349$	−2.32120	−	13.1642i	−0.124251	−	0.704661i	0.857499	−	0.514485i	$-0.172017\pi$
$350$	1.32491	+	7.74655i	0.0708195	+	0.414071i
$351$	−11.5788	+	9.22391i	−0.618032	+	0.492336i
$352$	23.1726	+	40.1361i	1.23510	+	2.13926i
$353$	8.39653	+	3.05609i	0.446902	+	0.162659i	0.555661	−	0.831409i	$-0.312465\pi$
$353$	8.39653	+	3.05609i	0.446902	+	0.162659i	−0.108758	+	0.994068i	$0.534688\pi$
$354$	−9.30446	−	32.0669i	−0.494526	−	1.70434i
$355$	20.5714	+	17.2614i	1.09181	+	0.916141i
$356$	−10.8827	−	9.13170i	−0.576784	−	0.483979i
$357$	−9.05675	+	20.2334i	−0.479334	+	1.07086i
$358$	−23.1431	−	8.42342i	−1.22315	−	0.445191i
$359$	6.48945	−	11.2401i	0.342500	−	0.593228i	−0.642396	−	0.766373i	$-0.722060\pi$
$359$	6.48945	−	11.2401i	0.342500	−	0.593228i	0.984896	+	0.173145i	$0.0553930\pi$
$360$	−0.715829	−	1.74009i	−0.0377275	−	0.0917110i
$361$	9.34560	+	16.1870i	0.491874	+	0.851950i
$362$	6.96633	+	2.53554i	0.366142	+	0.133265i
$363$	−15.2582	+	34.5630i	−0.800846	+	1.81409i
$364$	8.06674	−	13.8076i	0.422812	−	0.723717i
$365$	−0.201523	+	1.14290i	−0.0105482	+	0.0598219i
$366$	−17.9128	+	1.93978i	−0.936316	+	0.101394i
$367$	1.21615	+	6.89713i	0.0634825	+	0.360027i	0.999957	+	0.00929108i	$0.00295749\pi$
$367$	1.21615	+	6.89713i	0.0634825	+	0.360027i	−0.936474	+	0.350736i	$0.885931\pi$
$368$	5.13656	+	8.89679i	0.267762	+	0.463777i
$369$	32.8847	+	4.41055i	1.71191	+	0.229604i
$370$	21.0607	+	36.4781i	1.09489	+	1.89641i
$371$	12.4180	+	10.5292i	0.644711	+	0.546648i
$372$	−16.4803	+	8.10232i	−0.854462	+	0.420086i
$373$	−0.110958	+	0.629272i	−0.00574517	+	0.0325825i	−0.987546	−	0.157333i	$-0.949710\pi$
$373$	−0.110958	+	0.629272i	−0.00574517	+	0.0325825i	0.981800	+	0.189916i	$0.0608215\pi$
$374$	−9.76867	+	55.4009i	−0.505126	+	2.86471i
$375$	−4.33990	−	14.9570i	−0.224111	−	0.772378i
$376$	0.563477	−	0.472814i	0.0290591	−	0.0243835i
$377$	2.69123			0.138605
$378$	−5.68507	+	27.3248i	−0.292408	+	1.40544i
$379$	5.13223			0.263625			0.131813	−	0.991275i	$-0.457920\pi$
$379$	5.13223			0.263625			0.131813	+	0.991275i	$0.457920\pi$
$380$	2.29597	−	1.92655i	0.117781	−	0.0988299i
$381$	7.04803	+	1.73371i	0.361081	+	0.0888205i
$382$	0.580853	−	3.29418i	0.0297190	−	0.168545i
$383$	0.138926	−	0.787888i	0.00709878	−	0.0402592i	−0.981053	−	0.193741i	$-0.937938\pi$
$383$	0.138926	−	0.787888i	0.00709878	−	0.0402592i	0.988151	+	0.153482i	$0.0490488\pi$
$384$	2.83479	+	1.89912i	0.144662	+	0.0969142i
$385$	6.88551	−	37.9093i	0.350918	−	1.93204i
$386$	−7.65152	−	13.2528i	−0.389452	−	0.674550i
$387$	12.6724	+	13.8971i	0.644175	+	0.706427i
$388$	−6.26372	−	10.8491i	−0.317992	−	0.550779i
$389$	−3.85385	−	21.8563i	−0.195398	−	1.10816i	−0.911851	−	0.410521i	$-0.865347\pi$
$389$	−3.85385	−	21.8563i	−0.195398	−	1.10816i	0.716453	−	0.697635i	$-0.245764\pi$
$390$	10.2856	−	23.2990i	0.520830	−	1.17979i
$391$	−2.30601	+	13.0780i	−0.116620	+	0.661384i
$392$	−0.282383	−	1.70369i	−0.0142625	−	0.0860495i
$393$	−4.63175	+	0.501573i	−0.233641	+	0.0253010i
$394$	15.0293	+	5.47021i	0.757164	+	0.275585i
$395$	−4.19173	−	7.26030i	−0.210909	−	0.365305i
$396$	1.50189	+	36.4269i	0.0754727	+	1.83052i
$397$	0.0990744	−	0.171602i	0.00497240	−	0.00861246i	−0.863528	−	0.504300i	$-0.831751\pi$
$397$	0.0990744	−	0.171602i	0.00497240	−	0.00861246i	0.868501	+	0.495688i	$0.165084\pi$
$398$	1.88377	+	0.685637i	0.0944249	+	0.0343679i
$399$	−2.53313	+	0.261148i	−0.126815	+	0.0130738i
$400$	−4.19442	−	3.51953i	−0.209721	−	0.175977i
$401$	−10.4032	−	8.72931i	−0.519510	−	0.435921i	0.344951	−	0.938621i	$-0.387896\pi$
$401$	−10.4032	−	8.72931i	−0.519510	−	0.435921i	−0.864461	+	0.502700i	$0.832340\pi$
$402$	−23.1854	+	24.1610i	−1.15638	+	1.20504i
$403$	−13.3795	−	4.86975i	−0.666481	−	0.242579i
$404$	−3.30350	−	5.72182i	−0.164355	−	0.284671i
$405$	−2.10475	+	22.7835i	−0.104586	+	1.13212i
$406$	3.90352	−	3.24140i	0.193729	−	0.160868i
$407$	−8.11790	−	46.0389i	−0.402389	−	2.28206i
$408$	0.576016	+	1.98518i	0.0285170	+	0.0982811i
$409$	1.40459	−	7.96584i	0.0694526	−	0.393885i	−0.930188	−	0.367083i	$-0.880356\pi$
$409$	1.40459	−	7.96584i	0.0694526	−	0.393885i	0.999641	−	0.0268022i	$-0.00853244\pi$
$410$	−53.6390	+	19.5230i	−2.64904	+	0.964173i
$411$	−3.56125	+	1.75085i	−0.175664	+	0.0863629i
$412$	24.7958	+	9.02493i	1.22160	+	0.444627i
$413$	−4.23533	−	24.7633i	−0.208407	−	1.21852i
$414$	0.688768	+	16.7054i	0.0338511	+	0.821028i
$415$	6.45814			0.317018
$416$	4.00259	+	22.6998i	0.196243	+	1.11295i
$417$	1.49292	−	3.38179i	0.0731088	−	0.165607i
$418$	−6.07268	+	2.21027i	−0.297024	+	0.108108i
$419$	3.04268	−	17.2559i	0.148644	−	0.843005i	−0.815724	−	0.578442i	$-0.803661\pi$
$419$	3.04268	−	17.2559i	0.148644	−	0.843005i	0.964368	−	0.264563i	$-0.0852278\pi$
$420$	−6.76539	−	23.7721i	−0.330117	−	1.15996i
$421$	14.4084	−	12.0901i	0.702223	−	0.589235i	−0.220182	−	0.975459i	$-0.570665\pi$
$421$	14.4084	−	12.0901i	0.702223	−	0.589235i	0.922405	+	0.386223i	$0.126221\pi$
$422$	32.5759			1.58577
$423$	−8.73734	+	1.91479i	−0.424824	+	0.0931003i
$424$	1.51813			0.0737271
$425$	−1.22907	−	6.97039i	−0.0596185	−	0.338113i
$426$	−30.8582	−	20.6730i	−1.49508	−	1.00161i
$427$	−13.5565	−	0.0696737i	−0.656046	−	0.00337175i
$428$	14.8682	−	5.41158i	0.718681	−	0.261578i
$429$	−19.5714	+	20.3950i	−0.944916	+	0.984678i
$430$	−30.4049	−	11.0665i	−1.46626	−	0.533674i
$431$	−1.50044	+	2.59884i	−0.0722736	+	0.125182i	−0.899897	−	0.436102i	$-0.856359\pi$
$431$	−1.50044	+	2.59884i	−0.0722736	+	0.125182i	0.827624	+	0.561283i	$0.189692\pi$
$432$	−9.29072	−	17.0819i	−0.447000	−	0.821852i
$433$	−25.9071			−1.24502			−0.622508	−	0.782613i	$-0.713886\pi$
$433$	−25.9071			−1.24502			−0.622508	+	0.782613i	$0.713886\pi$
$434$	−25.2718	+	9.05135i	−1.21308	+	0.434479i
$435$	2.88002	−	3.00121i	0.138086	−	0.143897i
$436$	−24.8474	−	20.8494i	−1.18997	−	0.998506i
$437$	−1.43353	+	0.521761i	−0.0685748	+	0.0249592i
$438$	0.106927	−	1.60161i	0.00510915	−	0.0765278i
$439$	4.24499	+	24.0745i	0.202602	+	1.14901i	0.901168	+	0.433469i	$0.142711\pi$
$439$	4.24499	+	24.0745i	0.202602	+	1.14901i	−0.698566	+	0.715546i	$0.746178\pi$
$440$	−1.79636	−	3.11139i	−0.0856382	−	0.148330i
$441$	−6.56877	+	19.9462i	−0.312798	+	0.949820i
$442$	−13.9895	+	24.2305i	−0.665412	+	1.15253i
$443$	−4.17871	−	1.52093i	−0.198537	−	0.0722614i	0.240838	−	0.970565i	$-0.422578\pi$
$443$	−4.17871	−	1.52093i	−0.198537	−	0.0722614i	−0.439375	+	0.898304i	$0.644800\pi$
$444$	−17.7033	−	24.2058i	−0.840161	−	1.14876i
$445$	−13.0411	−	10.9428i	−0.618206	−	0.518736i
$446$	−11.0683	+	4.02852i	−0.524097	+	0.190756i
$447$	5.68100	−	12.8687i	0.268702	−	0.608668i
$448$	18.0426	+	15.2982i	0.852431	+	0.722773i
$449$	−2.20153	+	3.81316i	−0.103896	+	0.179954i	−0.913287	−	0.407317i	$-0.866464\pi$
$449$	−2.20153	+	3.81316i	−0.103896	+	0.179954i	0.809390	+	0.587271i	$0.199798\pi$
$450$	−3.39022	−	8.24123i	−0.159817	−	0.388495i
$451$	63.3529			2.98317
$452$	28.1626	−	23.6313i	1.32466	−	1.11152i
$453$	−23.1435	−	15.5047i	−1.08738	−	0.728473i
$454$	39.2632	+	32.9457i	1.84271	+	1.54622i
$455$	9.66659	−	16.5461i	0.453177	−	0.775691i
$456$	−0.164412	+	0.171330i	−0.00769927	+	0.00802326i
$457$	−31.8323	+	26.7105i	−1.48905	+	1.24946i	−0.593241	+	0.805025i	$0.702152\pi$
$457$	−31.8323	+	26.7105i	−1.48905	+	1.24946i	−0.895810	+	0.444438i	$0.853404\pi$
$458$	20.8960	−	36.1929i	0.976406	−	1.69118i
$459$	4.99348	−	24.6350i	0.233076	−	1.14986i
$460$	−7.40315	−	12.8226i	−0.345174	−	0.597858i
$461$	−4.35940	−	24.7234i	−0.203037	−	1.15148i	−0.900499	−	0.434859i	$-0.856798\pi$
$461$	−4.35940	−	24.7234i	−0.203037	−	1.15148i	0.697461	−	0.716623i	$-0.254313\pi$
$462$	−3.82320	+	53.1546i	−0.177871	+	2.47297i
$463$	21.8134	−	7.93944i	1.01376	−	0.368977i	0.218882	−	0.975751i	$-0.429759\pi$
$463$	21.8134	−	7.93944i	1.01376	−	0.368977i	0.794874	+	0.606774i	$0.207537\pi$
$464$	−0.613844	+	3.48128i	−0.0284970	+	0.161615i
$465$	−19.7487	+	9.70923i	−0.915825	+	0.450255i
$466$	−44.9756	+	37.7390i	−2.08346	+	1.74823i
$467$	3.42146	−	5.92613i	0.158326	−	0.274229i	−0.775939	−	0.630808i	$-0.782724\pi$
$467$	3.42146	−	5.92613i	0.158326	−	0.274229i	0.934265	+	0.356579i	$0.116057\pi$
$468$	−5.49449	+	17.2800i	−0.253983	+	0.798767i
$469$	−19.3839	+	16.0960i	−0.895066	+	0.743244i
$470$	11.7882	−	9.89151i	0.543751	−	0.456261i
$471$	−3.93532	+	8.91434i	−0.181330	+	0.410751i
$472$	−1.79454	−	1.50580i	−0.0826004	−	0.0693100i
$473$	27.5096	+	23.0833i	1.26489	+	1.06137i
$474$	6.84520	+	9.35946i	0.314410	+	0.429894i
$475$	0.622857	−	0.522639i	0.0285786	−	0.0239803i
$476$	4.57750	+	26.7639i	0.209809	+	1.22672i
$477$	−16.3543	−	8.56400i	−0.748811	−	0.392119i
$478$	14.0763	−	24.3809i	0.643836	−	1.11516i
$479$	−6.31239	+	5.29673i	−0.288421	+	0.242014i	−0.775505	−	0.631341i	$-0.782505\pi$
$479$	−6.31239	+	5.29673i	−0.288421	+	0.242014i	0.487085	+	0.873355i	$0.338060\pi$
$480$	29.5978	+	19.8286i	1.35095	+	0.905047i
$481$	4.03747	−	22.8976i	0.184093	−	1.04404i
$482$	15.4598	−	5.62690i	0.704174	−	0.256298i
$483$	−0.902511	+	12.5478i	−0.0410657	+	0.570942i
$484$	8.03585	+	45.5736i	0.365266	+	2.07153i
$485$	−7.50598	−	13.0007i	−0.340829	−	0.590333i
$486$	−0.498439	−	31.6430i	−0.0226096	−	1.43536i
$487$	−18.6466	+	32.2969i	−0.844958	+	1.46351i	0.0406993	+	0.999171i	$0.487041\pi$
$487$	−18.6466	+	32.2969i	−0.844958	+	1.46351i	−0.885658	+	0.464339i	$0.846292\pi$
$488$	−0.968362	+	0.812552i	−0.0438357	+	0.0367825i
$489$	−1.22019	−	0.300148i	−0.0551789	−	0.0135732i
$490$	−5.90759	−	35.6422i	−0.266878	−	1.61015i
$491$	3.56990	+	2.99550i	0.161107	+	0.135185i	0.719778	−	0.694205i	$-0.244244\pi$
$491$	3.56990	+	2.99550i	0.161107	+	0.135185i	−0.558670	+	0.829390i	$0.688688\pi$
$492$	36.4705	−	17.9303i	1.64422	−	0.808361i
$493$	−3.50050	+	2.93727i	−0.157655	+	0.132288i
$494$	−3.21411			−0.144610
$495$	1.79975	+	43.6513i	0.0808928	+	1.96198i
$496$	9.35108	−	16.1966i	0.419876	−	0.727247i
$497$	−21.3161	−	18.0738i	−0.956156	−	0.810721i
$498$	−8.88061	+	0.961683i	−0.397950	+	0.0430941i
$499$	2.08470	−	0.758770i	0.0933241	−	0.0339672i	−0.294936	−	0.955517i	$-0.595298\pi$
$499$	2.08470	−	0.758770i	0.0933241	−	0.0339672i	0.388260	+	0.921550i	$0.373076\pi$
$500$	−14.6130	−	12.2618i	−0.653513	−	0.548362i
$501$	−11.0396	+	1.19548i	−0.493211	+	0.0534099i
$502$	−5.59028	−	2.03469i	−0.249506	−	0.0908129i
$503$	6.91864	−	11.9834i	0.308487	−	0.534315i	−0.669545	−	0.742772i	$-0.733511\pi$
$503$	6.91864	−	11.9834i	0.308487	−	0.534315i	0.978032	+	0.208457i	$0.0668441\pi$
$504$	0.735648	+	1.81472i	0.0327684	+	0.0808342i
$505$	−3.95867	−	6.85661i	−0.176158	−	0.305115i
$506$	5.54368	+	31.4398i	0.246447	+	1.39767i
$507$	7.59046	−	3.73176i	0.337104	−	0.165733i
$508$	8.35405	−	3.04063i	0.370651	−	0.134906i
$509$	1.52005	+	1.27547i	0.0673751	+	0.0565344i	0.675853	−	0.737036i	$-0.263775\pi$
$509$	1.52005	+	1.27547i	0.0673751	+	0.0565344i	−0.608478	+	0.793571i	$0.708220\pi$
$510$	12.0505	+	41.5310i	0.533607	+	1.83903i
$511$	0.215836	−	1.18832i	0.00954802	−	0.0525682i
$512$	−32.1231			−1.41966
$513$	2.73764	−	0.918205i	0.120870	−	0.0405397i
$514$	17.6049	−	30.4926i	0.776520	−	1.34497i
$515$	29.7135	+	10.8148i	1.30933	+	0.476558i
$516$	22.3696	+	5.50258i	0.984766	+	0.242237i
$517$	−16.0492	+	5.84142i	−0.705842	+	0.256905i
$518$	−21.7225	−	38.0750i	−0.954431	−	1.67292i
$519$	28.0875	−	13.8089i	1.23290	−	0.606143i
$520$	−0.310284	−	1.75971i	−0.0136069	−	0.0771684i
$521$	28.4951			1.24839			0.624196	−	0.781268i	$-0.285427\pi$
$521$	28.4951			1.24839			0.624196	+	0.781268i	$0.285427\pi$
$522$	−3.51341	+	4.55583i	−0.153778	+	0.199403i
$523$	−41.5117			−1.81518			−0.907590	−	0.419857i	$-0.862080\pi$
$523$	−41.5117			−1.81518			−0.907590	+	0.419857i	$0.862080\pi$
$524$	−4.37137	+	3.66801i	−0.190964	+	0.160238i
$525$	−1.83533	−	6.44896i	−0.0801005	−	0.281456i
$526$	5.19530	−	29.4640i	0.226526	−	1.28469i
$527$	22.7178	−	8.26859i	0.989602	−	0.360186i
$528$	−21.9182	−	29.9688i	−0.953867	−	1.30423i
$529$	−2.68526	−	15.2289i	−0.116750	−	0.662124i
$530$	31.7602			1.37957
$531$	10.8375	+	26.3446i	0.470307	+	1.14326i
$532$	−2.39970	+	1.99266i	−0.104040	+	0.0863927i
$533$	29.6086	+	10.7767i	1.28249	+	0.466789i
$534$	19.5623	+	13.1055i	0.846544	+	0.567129i
$535$	17.8169	−	6.48483i	0.770293	−	0.280364i
$536$	−0.407966	+	2.31369i	−0.0176214	+	0.0999362i
$537$	20.4038	+	5.01903i	0.880490	+	0.216587i
$538$	−10.5992	−	60.1109i	−0.456963	−	2.59157i
$539$	−7.36844	+	39.4150i	−0.317381	+	1.69772i
$540$	13.3904	+	24.6195i	0.576230	+	1.05945i
$541$	6.73979	+	11.6737i	0.289766	+	0.501890i	0.973754	−	0.227604i	$-0.0730891\pi$
$541$	6.73979	+	11.6737i	0.289766	+	0.501890i	−0.683987	+	0.729494i	$0.739756\pi$
$542$	35.9069	+	13.0691i	1.54234	+	0.561364i
$543$	−6.14176	−	1.51078i	−0.263568	−	0.0648338i
$544$	−29.9813	−	25.1573i	−1.28544	−	1.07861i
$545$	−29.7753	−	24.9844i	−1.27543	−	1.07022i
$546$	−10.8287	+	24.1920i	−0.463425	+	1.03532i
$547$	−38.5140	−	14.0180i	−1.64674	−	0.599365i	−0.658543	−	0.752543i	$-0.728827\pi$
$547$	−38.5140	−	14.0180i	−1.64674	−	0.599365i	−0.988199	+	0.153178i	$0.951049\pi$
$548$	−2.43035	+	4.20949i	−0.103819	+	0.179821i
$549$	15.0155	−	3.29066i	0.640846	−	0.140442i
$550$	−8.50771	−	14.7358i	−0.362770	−	0.628336i
$551$	−0.493277	−	0.179538i	−0.0210143	−	0.00764858i
$552$	0.692487	+	0.946839i	0.0294742	+	0.0403002i
$553$	4.32346	+	7.57813i	0.183852	+	0.322255i
$554$	−10.6851	+	60.5982i	−0.453966	+	2.57457i
$555$	−21.2143	−	29.0064i	−0.900498	−	1.23125i
$556$	−0.786261	−	4.45911i	−0.0333449	−	0.189108i
$557$	2.11105	+	3.65645i	0.0894482	+	0.154929i	0.907278	−	0.420531i	$-0.138156\pi$
$557$	2.11105	+	3.65645i	0.0894482	+	0.154929i	−0.817830	+	0.575460i	$0.804823\pi$
$558$	25.7107	−	16.2920i	1.08842	−	0.689695i
$559$	8.93030	+	15.4677i	0.377711	+	0.654215i
$560$	19.1986	+	16.2784i	0.811287	+	0.687887i
$561$	3.19713	−	47.8885i	0.134983	−	2.02186i
$562$	1.67844	−	9.51893i	0.0708009	−	0.401532i
$563$	−5.09575	+	28.8994i	−0.214760	+	1.21797i	0.666562	+	0.745450i	$0.267765\pi$
$563$	−5.09575	+	28.8994i	−0.214760	+	1.21797i	−0.881322	+	0.472516i	$0.843346\pi$
$564$	−7.58581	+	7.90502i	−0.319420	+	0.332861i
$565$	33.7480	−	28.3180i	1.41979	−	1.19135i
$566$	19.9614			0.839041
$567$	2.31225	−	23.6992i	0.0971054	−	0.995274i
$568$	−2.60595			−0.109343
$569$	−8.40773	+	7.05492i	−0.352470	+	0.295758i	−0.801781	−	0.597618i	$-0.796114\pi$
$569$	−8.40773	+	7.05492i	−0.352470	+	0.295758i	0.449311	+	0.893376i	$0.351670\pi$
$570$	−3.43958	+	3.58431i	−0.144068	+	0.150130i
$571$	−1.29682	+	7.35465i	−0.0542704	+	0.307783i	−0.999845	−	0.0176236i	$-0.994390\pi$
$571$	−1.29682	+	7.35465i	−0.0542704	+	0.307783i	0.945574	+	0.325406i	$0.105501\pi$
$572$	−6.01214	+	34.0965i	−0.251380	+	1.42565i
$573$	−0.190104	+	2.84749i	−0.00794171	+	0.118956i
$574$	55.9260	−	20.0305i	2.33431	−	0.836056i
$575$	−2.00834	−	3.47855i	−0.0837538	−	0.145066i
$576$	−23.7617	−	12.4429i	−0.990072	−	0.518456i
$577$	−3.85645	−	6.67956i	−0.160546	−	0.278074i	0.774519	−	0.632551i	$-0.217992\pi$
$577$	−3.85645	−	6.67956i	−0.160546	−	0.278074i	−0.935065	+	0.354477i	$0.884659\pi$
$578$	−2.25644	−	12.7969i	−0.0938555	−	0.532281i
$579$	7.70735	+	10.5383i	0.320306	+	0.437956i
$580$	0.884712	−	5.01745i	0.0367357	−	0.208338i
$581$	−6.72091	−	0.0345421i	−0.278831	−	0.00143305i
$582$	12.2574	+	16.7596i	0.508088	+	0.694710i
$583$	−33.1238	−	12.0561i	−1.37185	−	0.499312i
$584$	−0.0563095	−	0.0975308i	−0.00233010	−	0.00403585i
$585$	−6.58419	+	20.7070i	−0.272223	+	0.856131i
$586$	21.1561	−	36.6435i	0.873952	−	1.51373i
$587$	−11.7083	−	4.26146i	−0.483252	−	0.175889i	0.0888943	−	0.996041i	$-0.471667\pi$
$587$	−11.7083	−	4.26146i	−0.483252	−	0.175889i	−0.572146	+	0.820152i	$0.693889\pi$
$588$	6.91352	+	24.7756i	0.285109	+	1.02173i
$589$	2.12747	+	1.78516i	0.0876607	+	0.0735561i
$590$	−37.5427	−	31.5021i	−1.54561	−	1.29692i
$591$	−13.2504	−	3.25938i	−0.545047	−	0.134073i
$592$	28.6987	+	10.4455i	1.17951	+	0.429307i
$593$	8.24951	+	14.2886i	0.338767	+	0.586761i	0.984201	−	0.177055i	$-0.0566569\pi$
$593$	8.24951	+	14.2886i	0.338767	+	0.586761i	−0.645434	+	0.763816i	$0.723324\pi$
$594$	−8.97498	−	59.7571i	−0.368248	−	2.45186i
$595$	5.48534	+	32.0719i	0.224877	+	1.31482i
$596$	−2.99195	−	16.9682i	−0.122555	−	0.695044i
$597$	−1.66080	−	0.408531i	−0.0679720	−	0.0167201i
$598$	−2.75718	+	15.6367i	−0.112749	+	0.639433i
$599$	41.2606	−	15.0176i	1.68586	−	0.613604i	0.691769	−	0.722118i	$-0.256831\pi$
$599$	41.2606	−	15.0176i	1.68586	−	0.613604i	0.994095	+	0.108514i	$0.0346092\pi$
$600$	−0.519427	−	0.347982i	−0.0212055	−	0.0142063i
$601$	−30.4547	−	11.0846i	−1.24227	−	0.452151i	−0.364490	−	0.931207i	$-0.618757\pi$
$601$	−30.4547	−	11.0846i	−1.24227	−	0.452151i	−0.877784	+	0.479057i	$0.840979\pi$
$602$	31.5829	+	11.6794i	1.28722	+	0.476017i
$603$	17.4467	−	22.6231i	0.710485	−	0.921285i
$604$	−34.1211			−1.38837
$605$	9.62957	+	54.6120i	0.391498	+	2.22029i
$606$	6.46460	+	8.83906i	0.262606	+	0.359062i
$607$	39.2272	−	14.2775i	1.59218	−	0.579507i	0.614376	−	0.789013i	$-0.289408\pi$
$607$	39.2272	−	14.2775i	1.59218	−	0.579507i	0.977807	+	0.209506i	$0.0671855\pi$
$608$	0.780721	−	4.42769i	0.0316624	−	0.179566i
$609$	−3.01325	+	3.10792i	−0.122103	+	0.125939i
$610$	−20.2586	+	16.9990i	−0.820248	+	0.688270i
$611$	−8.49440			−0.343647
$612$	−11.7130	−	28.4730i	−0.473471	−	1.15095i
$613$	−38.2771			−1.54600			−0.772999	−	0.634408i	$-0.781244\pi$
$613$	−38.2771			−1.54600			−0.772999	+	0.634408i	$0.781244\pi$
$614$	−11.4677	−	65.0365i	−0.462799	−	2.62466i
$615$	43.7036	−	21.4864i	1.76230	−	0.866414i
$616$	1.85281	+	3.24760i	0.0746519	+	0.130849i
$617$	31.1195	−	11.3266i	1.25282	−	0.455990i	0.371469	−	0.928445i	$-0.378854\pi$
$617$	31.1195	−	11.3266i	1.25282	−	0.455990i	0.881355	+	0.472455i	$0.156632\pi$
$618$	−42.4695	−	10.4469i	−1.70837	−	0.420234i
$619$	−9.82447	−	3.57581i	−0.394879	−	0.143724i	0.136946	−	0.990579i	$-0.456271\pi$
$619$	−9.82447	−	3.57581i	−0.394879	−	0.143724i	−0.531825	+	0.846854i	$0.678494\pi$
$620$	−13.4774	+	23.3435i	−0.541265	+	0.937498i
$621$	−2.11865	−	14.1064i	−0.0850184	−	0.566068i
$622$	12.8718			0.516112
$623$	13.5132	+	11.4578i	0.541394	+	0.459045i
$624$	−5.14584	−	17.7346i	−0.205998	−	0.709954i
$625$	−23.1154	−	19.3961i	−0.924614	−	0.775844i
$626$	51.8406	−	18.8684i	2.07197	−	0.754134i
$627$	4.94785	−	2.43255i	0.197598	−	0.0971467i
$628$	2.07257	+	11.7541i	0.0827046	+	0.469041i
$629$	19.7394	+	34.1897i	0.787063	+	1.36323i
$630$	15.3901	+	37.9650i	0.613158	+	1.51256i
$631$	3.39863	−	5.88659i	0.135297	−	0.234342i	−0.790414	−	0.612573i	$-0.790134\pi$
$631$	3.39863	−	5.88659i	0.135297	−	0.234342i	0.925711	+	0.378232i	$0.123468\pi$
$632$	0.764479	+	0.278248i	0.0304093	+	0.0110681i
$633$	−27.6310	+	2.99217i	−1.09823	+	0.118928i
$634$	6.06089	+	5.08569i	0.240709	+	0.201979i
$635$	10.0109	−	3.64366i	0.397270	−	0.144594i
$636$	−22.4806	+	2.43443i	−0.891414	+	0.0965314i
$637$	−10.1484	+	17.1676i	−0.402095	+	0.680205i
$638$	−5.49267	+	9.51358i	−0.217457	+	0.376646i
$639$	28.0729	+	14.7005i	1.11055	+	0.581543i
$640$	5.00828			0.197970
$641$	−3.75248	+	3.14871i	−0.148214	+	0.124367i	−0.713880	−	0.700268i	$-0.753064\pi$
$641$	−3.75248	+	3.14871i	−0.148214	+	0.124367i	0.565666	+	0.824635i	$0.308619\pi$
$642$	−23.5345	+	11.5704i	−0.928831	+	0.456649i
$643$	−16.7039	−	14.0162i	−0.658736	−	0.552745i	0.250972	−	0.967994i	$-0.419250\pi$
$643$	−16.7039	−	14.0162i	−0.658736	−	0.552745i	−0.909708	+	0.415249i	$0.863694\pi$
$644$	7.63579	+	13.3840i	0.300892	+	0.527402i
$645$	26.8061	+	6.59388i	1.05549	+	0.259634i
$646$	4.18061	−	3.50795i	0.164484	−	0.138018i
$647$	20.0922	−	34.8007i	0.789906	−	1.36816i	−0.136118	−	0.990693i	$-0.543462\pi$
$647$	20.0922	−	34.8007i	0.789906	−	1.36816i	0.926024	−	0.377465i	$-0.123204\pi$
$648$	−1.26470	−	1.82496i	−0.0496820	−	0.0716913i
$649$	27.1965	+	47.1058i	1.06756	+	1.84906i
$650$	−1.46953	−	8.33413i	−0.0576398	−	0.326892i
$651$	20.6042	−	9.99866i	0.807543	−	0.391878i
$652$	−1.44629	+	0.526408i	−0.0566413	+	0.0206157i
$653$	−0.728550	+	4.13181i	−0.0285104	+	0.161690i	−0.995739	−	0.0922169i	$-0.970605\pi$
$653$	−0.728550	+	4.13181i	−0.0285104	+	0.161690i	0.967229	+	0.253907i	$0.0817158\pi$
$654$	44.6645	+	29.9223i	1.74652	+	1.17006i
$655$	−5.23832	+	4.39548i	−0.204678	+	0.171745i
$656$	−20.6938	+	35.8427i	−0.807957	+	1.39942i
$657$	0.0564157	+	1.36831i	0.00220099	+	0.0533829i
$658$	−12.3208	+	10.2309i	−0.480315	+	0.398843i
$659$	−2.95798	+	2.48204i	−0.115226	+	0.0966864i	−0.698580	−	0.715532i	$-0.746185\pi$
$659$	−2.95798	+	2.48204i	−0.115226	+	0.0966864i	0.583354	+	0.812218i	$0.301740\pi$
$660$	31.5899	+	43.1930i	1.22964	+	1.68129i
$661$	−1.93691	−	1.62526i	−0.0753372	−	0.0632155i	0.604341	−	0.796725i	$-0.293436\pi$
$661$	−1.93691	−	1.62526i	−0.0753372	−	0.0632155i	−0.679679	+	0.733510i	$0.737881\pi$
$662$	−43.4098	−	36.4252i	−1.68717	−	1.41570i
$663$	9.64031	−	21.8374i	0.374398	−	0.848093i
$664$	−0.480084	+	0.402839i	−0.0186309	+	0.0156332i
$665$	−2.87562	+	2.38785i	−0.111512	+	0.0925970i
$666$	33.4912	+	36.7278i	1.29776	+	1.42317i
$667$	−1.29661	+	2.24579i	−0.0502049	+	0.0869574i
$668$	−10.4189	+	8.74253i	−0.403121	+	0.338259i
$669$	9.01812	−	4.43365i	0.348660	−	0.171415i
$670$	−8.53486	+	48.4036i	−0.329731	+	1.86999i
$671$	27.5812	−	10.0387i	1.06476	−	0.387541i
$672$	−30.6960	−	20.7937i	−1.18413	−	0.802135i
$673$	5.48831	+	31.1257i	0.211559	+	1.19981i	0.886779	+	0.462193i	$0.152937\pi$
$673$	5.48831	+	31.1257i	0.211559	+	1.19981i	−0.675220	+	0.737616i	$0.735952\pi$
$674$	−2.51286	−	4.35240i	−0.0967917	−	0.167648i
$675$	3.63258	+	6.67884i	0.139818	+	0.257069i
$676$	5.18005	−	8.97211i	0.199233	−	0.345081i
$677$	−34.7742	+	29.1790i	−1.33648	+	1.12144i	−0.353964	+	0.935259i	$0.615167\pi$
$677$	−34.7742	+	29.1790i	−1.33648	+	1.12144i	−0.982516	+	0.186181i	$0.940389\pi$
$678$	−42.1902	+	43.9656i	−1.62031	+	1.68849i
$679$	7.74186	+	13.5699i	0.297105	+	0.520764i
$680$	2.32418	+	1.95021i	0.0891281	+	0.0747873i
$681$	−36.3293	−	24.3383i	−1.39214	−	0.932644i
$682$	44.5217	−	37.3581i	1.70482	−	1.43052i
$683$	−34.2783			−1.31162			−0.655811	−	0.754925i	$-0.727673\pi$
$683$	−34.2783			−1.31162			−0.655811	+	0.754925i	$0.727673\pi$
$684$	2.15987	−	2.80071i	0.0825848	−	0.107088i
$685$	−2.91235	+	5.04434i	−0.111275	+	0.192735i
$686$	5.95733	+	37.1240i	0.227452	+	1.41740i
$687$	−14.3997	+	32.6183i	−0.549381	+	1.24447i
$688$	−22.0455	+	8.02389i	−0.840475	+	0.305908i
$689$	−13.4299	−	11.2691i	−0.511640	−	0.429317i
$690$	14.4872	+	19.8084i	0.551518	+	0.754092i
$691$	16.9571	+	6.17189i	0.645080	+	0.234790i	0.643782	−	0.765209i	$-0.277365\pi$
$691$	16.9571	+	6.17189i	0.645080	+	0.234790i	0.00129822	+	0.999999i	$0.499587\pi$
$692$	19.1681	−	33.2001i	0.728662	−	1.26208i
$693$	−1.63951	−	45.4371i	−0.0622797	−	1.72601i
$694$	−22.0345	−	38.1648i	−0.836417	−	1.44872i
$695$	−0.942198	−	5.34347i	−0.0357396	−	0.202689i
$696$	−0.0268884	+	0.402750i	−0.00101920	+	0.0152662i
$697$	−50.2741	+	18.2983i	−1.90427	+	0.693096i
$698$	20.7885	+	17.4437i	0.786858	+	0.660252i
$699$	34.6821	−	36.1415i	1.31180	−	1.36700i
$700$	−6.26410	−	5.31131i	−0.236761	−	0.200749i
$701$	22.9450			0.866620			0.433310	−	0.901245i	$-0.357345\pi$
$701$	22.9450			0.866620			0.433310	+	0.901245i	$0.357345\pi$
$702$	5.97045	−	29.4548i	0.225340	−	1.11170i
$703$	−2.26759	+	3.92757i	−0.0855236	+	0.148131i
$704$	−48.1268	−	17.5167i	−1.81385	−	0.660186i
$705$	−9.09028	+	9.47280i	−0.342360	+	0.356766i
$706$	−17.0462	+	6.20433i	−0.641544	+	0.233503i
$707$	4.08307	+	7.15677i	0.153560	+	0.269158i
$708$	28.9883	+	19.4203i	1.08945	+	0.729858i
$709$	−2.63518	−	14.9449i	−0.0989664	−	0.561266i	−0.993460	−	0.114185i	$-0.963574\pi$
$709$	−2.63518	−	14.9449i	−0.0989664	−	0.561266i	0.894493	−	0.447082i	$-0.147537\pi$
$710$	−54.5178			−2.04601
$711$	−6.66581	−	7.30999i	−0.249987	−	0.274146i
$712$	1.65202			0.0619121
$713$	10.5099	−	8.81881i	0.393597	−	0.330267i
$714$	−12.3187	−	43.2853i	−0.461017	−	1.61991i
$715$	−7.20450	+	40.8588i	−0.269433	+	1.52803i
$716$	24.1847	−	8.80252i	0.903825	−	0.328965i
$717$	−9.70015	+	21.9729i	−0.362259	+	0.820593i
$718$	4.57548	+	25.9488i	0.170755	+	0.968402i
$719$	−42.4405			−1.58276			−0.791381	−	0.611323i	$-0.790638\pi$
$719$	−42.4405			−1.58276			−0.791381	+	0.611323i	$0.790638\pi$
$720$	−25.2842	−	13.2402i	−0.942285	−	0.493432i
$721$	−30.8646	−	11.4138i	−1.14946	−	0.425072i
$722$	−35.6576	−	12.9783i	−1.32704	−	0.483002i
$723$	−12.5962	+	6.19278i	−0.468458	+	0.230312i
$724$	−7.27985	+	2.64965i	−0.270554	+	0.0984735i
$725$	0.240007	−	1.36115i	0.00891363	−	0.0505517i
$726$	−21.3740	−	73.6632i	−0.793262	−	2.73390i
$727$	1.22040	+	6.92123i	0.0452621	+	0.256694i	0.999039	−	0.0438200i	$-0.0139528\pi$
$727$	1.22040	+	6.92123i	0.0452621	+	0.256694i	−0.953777	+	0.300514i	$0.902842\pi$
$728$	0.313497	+	1.83297i	0.0116190	+	0.0679344i
$729$	3.32926	+	26.7940i	0.123306	+	0.992369i
$730$	−1.17802	−	2.04040i	−0.0436006	−	0.0755185i
$731$	−28.4975	−	10.3722i	−1.05402	−	0.383632i
$732$	13.0366	−	13.5851i	0.481845	−	0.502121i
$733$	25.1453	+	21.0994i	0.928763	+	0.779325i	0.975595	−	0.219578i	$-0.0704680\pi$
$733$	25.1453	+	21.0994i	0.928763	+	0.779325i	−0.0468316	+	0.998903i	$0.514912\pi$
$734$	−10.8918	−	9.13930i	−0.402024	−	0.337338i
$735$	8.28466	+	29.6892i	0.305584	+	1.09510i
$736$	−20.8711	−	7.59645i	−0.769318	−	0.280009i
$737$	27.2752	−	47.2420i	1.00469	−	1.74018i
$738$	−56.8974	+	36.0539i	−2.09442	+	1.32716i
$739$	−2.89676	−	5.01734i	−0.106559	−	0.184566i	0.807815	−	0.589436i	$-0.200650\pi$
$739$	−2.89676	−	5.01734i	−0.106559	−	0.184566i	−0.914374	+	0.404870i	$0.867317\pi$
$740$	−41.3624	−	15.0547i	−1.52051	−	0.553422i
$741$	2.72622	−	0.295223i	0.100150	−	0.0108453i
$742$	−33.0525	−	0.169873i	−1.21339	−	0.00623623i
$743$	3.82255	−	21.6788i	0.140236	−	0.795317i	−0.830834	−	0.556521i	$-0.812136\pi$
$743$	3.82255	−	21.6788i	0.140236	−	0.795317i	0.971070	−	0.238797i	$-0.0767529\pi$
$744$	0.862447	−	1.95363i	0.0316188	−	0.0716235i
$745$	−3.58533	−	20.3334i	−0.131356	−	0.744959i
$746$	−0.648613	−	1.12343i	−0.0237474	−	0.0411317i
$747$	7.44424	−	1.63141i	0.272370	−	0.0596901i
$748$	−29.3937	−	50.9113i	−1.07474	−	1.86150i
$749$	−18.5766	+	6.65340i	−0.678773	+	0.243110i
$750$	26.2676	+	17.5976i	0.959159	+	0.642574i
$751$	5.94584	−	33.7206i	0.216967	−	1.23048i	−0.660494	−	0.750832i	$-0.729653\pi$
$751$	5.94584	−	33.7206i	0.216967	−	1.23048i	0.877461	−	0.479649i	$-0.159236\pi$
$752$	1.93749	−	10.9881i	0.0706531	−	0.400694i
$753$	4.92859	+	1.21236i	0.179608	+	0.0441807i
$754$	−4.18536	+	3.51194i	−0.152422	+	0.127897i
$755$	−40.8882			−1.48807
$756$	−13.8035	−	25.6929i	−0.502030	−	0.934440i
$757$	7.63111			0.277357			0.138679	−	0.990337i	$-0.455714\pi$
$757$	7.63111			0.277357			0.138679	+	0.990337i	$0.455714\pi$
$758$	−7.98158	+	6.69734i	−0.289904	+	0.243259i
$759$	−7.58999	−	26.1581i	−0.275499	−	0.949481i
$760$	−0.0605221	+	0.343238i	−0.00219537	+	0.0124506i
$761$	8.38957	−	47.5796i	0.304122	−	1.72476i	−0.323489	−	0.946232i	$-0.604856\pi$
$761$	8.38957	−	47.5796i	0.304122	−	1.72476i	0.627611	−	0.778527i	$-0.284033\pi$
$762$	−13.2234	+	6.50114i	−0.479034	+	0.235511i
$763$	30.8532	+	26.1603i	1.11696	+	0.947065i
$764$	1.74777	+	3.02723i	0.0632321	+	0.109521i
$765$	−14.0360	−	34.1199i	−0.507474	−	1.23361i
$766$	0.812104	+	1.40661i	0.0293425	+	0.0508227i
$767$	4.69764	+	26.6416i	0.169622	+	0.961974i
$768$	23.9050	−	2.58868i	0.862599	−	0.0934110i
$769$	−4.98810	+	28.2889i	−0.179875	+	1.02012i	0.752489	+	0.658604i	$0.228853\pi$
$769$	−4.98810	+	28.2889i	−0.179875	+	1.02012i	−0.932365	+	0.361519i	$0.882258\pi$
$770$	38.7618	+	67.9414i	1.39688	+	2.44844i
$771$	−12.1318	+	27.4810i	−0.436914	+	0.989705i
$772$	15.0273	+	5.46950i	0.540845	+	0.196852i
$773$	−0.858660	−	1.48724i	−0.0308839	−	0.0534924i	0.850170	−	0.526508i	$-0.176499\pi$
$773$	−0.858660	−	1.48724i	−0.0308839	−	0.0534924i	−0.881054	+	0.473015i	$0.843166\pi$
$774$	−37.8430	−	5.07557i	−1.36024	−	0.182438i
$775$	−3.65618	+	6.33269i	−0.131334	+	0.227477i
$776$	1.36892	+	0.498248i	0.0491415	+	0.0178861i
$777$	21.9224	+	30.3001i	0.786461	+	1.08701i
$778$	34.5149	+	28.9615i	1.23742	+	1.03832i
$779$	−4.70805	−	3.95052i	−0.168683	−	0.141542i
$780$	7.41652	+	25.5603i	0.265554	+	0.915206i
$781$	56.8585	+	20.6948i	2.03456	+	0.740518i
$782$	−13.4800	−	23.3480i	−0.482043	−	0.834924i
$783$	2.56163	−	4.18699i	0.0915450	−	0.149631i
$784$	−19.8927	−	17.0434i	−0.710452	−	0.608693i
$785$	2.48362	+	14.0853i	0.0886441	+	0.502726i
$786$	6.54871	−	6.82427i	0.233585	−	0.243414i
$787$	−4.68669	+	26.5795i	−0.167062	+	0.947457i	0.779850	+	0.625966i	$0.215295\pi$
$787$	−4.68669	+	26.5795i	−0.167062	+	0.947457i	−0.946913	+	0.321491i	$0.895816\pi$
$788$	−15.7057	+	5.71640i	−0.559492	+	0.203638i
$789$	−1.70034	+	25.4687i	−0.0605337	+	0.906709i
$790$	15.9933	+	5.82109i	0.569016	+	0.207105i
$791$	−35.2727	+	29.2897i	−1.25415	+	1.04142i
$792$	−2.85662	−	3.13268i	−0.101506	−	0.111315i
$793$	14.5980			0.518391
$794$	0.0698539	+	0.396161i	0.00247902	+	0.0140592i
$795$	−26.9391	+	2.91724i	−0.955431	+	0.103464i
$796$	−1.96855	+	0.716494i	−0.0697734	+	0.0253955i
$797$	−2.90591	+	16.4802i	−0.102933	+	0.583760i	0.889093	+	0.457726i	$0.151336\pi$
$797$	−2.90591	+	16.4802i	−0.102933	+	0.583760i	−0.992026	+	0.126034i	$0.959775\pi$
$798$	3.59870	−	3.71176i	0.127393	−	0.131395i
$799$	11.0487	−	9.27098i	0.390876	−	0.327984i
$800$	11.8379			0.418532
$801$	−17.7966	−	9.31927i	−0.628812	−	0.329280i
$802$	27.5703			0.973540
$803$	0.454073	+	2.57518i	0.0160239	+	0.0908760i
$804$	2.33102	−	34.9154i	0.0822088	−	1.23137i
$805$	9.15017	+	16.0384i	0.322501	+	0.565278i
$806$	27.1625	−	9.88633i	0.956757	−	0.348231i
$807$	14.5116	+	50.0128i	0.510832	+	1.76053i
$808$	0.721973	+	0.262777i	0.0253989	+	0.00924445i
$809$	−3.95309	+	6.84695i	−0.138983	+	0.240726i	−0.927112	−	0.374784i	$-0.877717\pi$
$809$	−3.95309	+	6.84695i	−0.138983	+	0.240726i	0.788129	+	0.615510i	$0.211050\pi$
$810$	−26.4581	−	38.1792i	−0.929645	−	1.34148i
$811$	35.7609			1.25574			0.627868	−	0.778320i	$-0.283928\pi$
$811$	35.7609			1.25574			0.627868	+	0.778320i	$0.283928\pi$
$812$	−0.947546	+	5.21687i	−0.0332523	+	0.183076i
$813$	−31.6568	−	7.78709i	−1.11025	−	0.273105i
$814$	72.7036	+	61.0056i	2.54826	+	2.13824i
$815$	−1.73313	+	0.630809i	−0.0607090	+	0.0220963i
$816$	26.0492	+	17.4513i	0.911905	+	0.610917i
$817$	−0.604951	−	3.43085i	−0.0211646	−	0.120030i
$818$	8.21067	+	14.2213i	0.287079	+	0.497236i
$819$	6.96284	−	21.5144i	0.243301	−	0.751773i
$820$	29.8252	−	51.6588i	1.04154	−	1.80400i
$821$	30.5943	+	11.1354i	1.06775	+	0.388629i	0.815334	−	0.578991i	$-0.196553\pi$
$821$	30.5943	+	11.1354i	1.06775	+	0.388629i	0.252414	+	0.967619i	$0.418776\pi$
$822$	3.25363	−	7.37017i	0.113483	−	0.257064i
$823$	16.6425	+	13.9647i	0.580120	+	0.486778i	0.884987	−	0.465617i	$-0.154167\pi$
$823$	16.6425	+	13.9647i	0.580120	+	0.486778i	−0.304867	+	0.952395i	$0.598612\pi$
$824$	−2.88343	+	1.04948i	−0.100449	+	0.0365605i
$825$	8.56979	+	11.7175i	0.298362	+	0.407951i
$826$	38.9018	+	32.9847i	1.35357	+	1.14768i
$827$	−8.58158	+	14.8637i	−0.298411	+	0.516863i	−0.975773	−	0.218787i	$-0.929790\pi$
$827$	−8.58158	+	14.8637i	−0.298411	+	0.516863i	0.677362	+	0.735650i	$0.263123\pi$
$828$	−11.7727	−	12.9104i	−0.409129	−	0.448667i
$829$	−12.7054			−0.441276			−0.220638	−	0.975356i	$-0.570814\pi$
$829$	−12.7054			−0.441276			−0.220638	+	0.975356i	$0.570814\pi$
$830$	−10.0436	+	8.42760i	−0.348619	+	0.292526i
$831$	3.49706	−	52.3811i	0.121312	−	1.81708i
$832$	−19.5129	−	16.3732i	−0.676486	−	0.567640i
$833$	−5.53699	−	33.4062i	−0.191845	−	1.15746i
$834$	2.09132	+	7.20752i	0.0724164	+	0.249576i
$835$	−12.4853	+	10.4764i	−0.432072	+	0.362551i
$836$	3.37663	−	5.84849i	0.116783	−	0.202274i
$837$	−20.3115	+	16.1805i	−0.702068	+	0.559280i
$838$	17.7862	+	30.8067i	0.614416	+	1.06420i
$839$	3.40606	+	19.3167i	0.117590	+	0.666887i	0.985435	+	0.170052i	$0.0543936\pi$
$839$	3.40606	+	19.3167i	0.117590	+	0.666887i	−0.867845	+	0.496835i	$0.834495\pi$
$840$	2.37958	+	1.61195i	0.0821034	+	0.0556174i
$841$	26.4126	−	9.61339i	0.910778	−	0.331496i
$842$	−6.63073	+	37.6047i	−0.228510	+	1.29594i
$843$	−0.549328	+	8.22816i	−0.0189199	+	0.283393i
$844$	−26.0777	+	21.8818i	−0.897631	+	0.753202i
$845$	6.20739	−	10.7515i	0.213541	−	0.369864i
$846$	11.0895	−	14.3797i	0.381264	−	0.494385i
$847$	−9.72929	−	56.8856i	−0.334302	−	1.95461i
$848$	17.6405	−	14.8022i	0.605778	−	0.508308i
$849$	−16.9314	+	1.83350i	−0.581083	+	0.0629256i
$850$	11.0075	+	9.23638i	0.377554	+	0.316805i
$851$	17.1625	+	14.4011i	0.588324	+	0.493663i
$852$	38.5890	−	4.17881i	1.32204	−	0.143164i
$853$	−26.1797	+	21.9674i	−0.896376	+	0.752149i	−0.969479	−	0.245175i	$-0.921154\pi$
$853$	−26.1797	+	21.9674i	−0.896376	+	0.752149i	0.0731024	+	0.997324i	$0.476710\pi$
$854$	21.1739	−	17.5823i	0.724554	−	0.601655i
$855$	2.58823	−	3.35616i	0.0885157	−	0.114778i
$856$	−0.919969	+	1.59343i	−0.0314439	+	0.0544624i
$857$	1.99806	−	1.67657i	0.0682524	−	0.0572706i	−0.608023	−	0.793919i	$-0.708037\pi$
$857$	1.99806	−	1.67657i	0.0682524	−	0.0572706i	0.676276	+	0.736649i	$0.263593\pi$
$858$	3.82265	−	57.2578i	0.130503	−	1.95475i
$859$	0.897983	−	5.09272i	0.0306388	−	0.173761i	−0.965649	−	0.259852i	$-0.916326\pi$
$859$	0.897983	−	5.09272i	0.0306388	−	0.173761i	0.996287	+	0.0860905i	$0.0274374\pi$
$860$	31.7733	−	11.5645i	1.08346	−	0.394348i
$861$	−45.5968	+	22.1269i	−1.55393	+	0.754081i
$862$	−1.05791	−	5.99969i	−0.0360324	−	0.204350i
$863$	21.0794	+	36.5106i	0.717552	+	1.24284i	0.961967	+	0.273166i	$0.0880707\pi$
$863$	21.0794	+	36.5106i	0.717552	+	1.24284i	−0.244415	+	0.969671i	$0.578596\pi$
$864$	39.1260	+	15.3795i	1.33109	+	0.523220i
$865$	22.9697	−	39.7846i	0.780992	−	1.35272i
$866$	40.2904	−	33.8077i	1.36912	−	1.14883i
$867$	3.08934	+	10.6471i	0.104920	+	0.361595i
$868$	14.1506	−	24.2212i	0.480303	−	0.822123i
$869$	−14.4703	−	12.1420i	−0.490872	−	0.411890i
$870$	−0.562519	+	8.42574i	−0.0190712	+	0.285659i
$871$	20.7835	−	17.4394i	0.704221	−	0.590911i
$872$	3.77188			0.127732
$873$	−11.9362	−	13.0897i	−0.403980	−	0.443020i
$874$	1.54853	−	2.68213i	0.0523797	−	0.0907242i
$875$	18.1451	+	15.3851i	0.613415	+	0.520112i
$876$	0.990230	+	1.35394i	0.0334568	+	0.0457456i
$877$	41.7115	−	15.1817i	1.40850	−	0.512651i	0.477808	−	0.878464i	$-0.341432\pi$
$877$	41.7115	−	15.1817i	1.40850	−	0.512651i	0.930688	+	0.365814i	$0.119209\pi$
$878$	−38.0180	−	31.9009i	−1.28304	−	1.07660i
$879$	−14.5789	+	33.0244i	−0.491735	+	1.11389i
$880$	−51.2103	−	18.6390i	−1.72630	−	0.628321i
$881$	−10.1994	+	17.6658i	−0.343625	+	0.595176i	−0.985103	−	0.171966i	$-0.944988\pi$
$881$	−10.1994	+	17.6658i	−0.343625	+	0.595176i	0.641478	+	0.767141i	$0.278322\pi$
$882$	−15.8133	−	39.5921i	−0.532461	−	1.33313i
$883$	−11.3979	−	19.7418i	−0.383571	−	0.664364i	0.607999	−	0.793938i	$-0.291972\pi$
$883$	−11.3979	−	19.7418i	−0.383571	−	0.664364i	−0.991570	+	0.129574i	$0.958639\pi$
$884$	−5.07715	−	28.7940i	−0.170763	−	0.968446i
$885$	34.7374	+	23.2718i	1.16769	+	0.782273i
$886$	8.48342	−	3.08771i	0.285006	−	0.103734i
$887$	−6.02600	−	5.05642i	−0.202333	−	0.169778i	0.535991	−	0.844224i	$-0.319938\pi$
$887$	−6.02600	−	5.05642i	−0.202333	−	0.169778i	−0.738324	+	0.674446i	$0.764383\pi$
$888$	3.38636	+	0.832992i	0.113639	+	0.0279534i
$889$	−10.4377	+	3.73838i	−0.350069	+	0.125381i
$890$	34.5611			1.15849
$891$	13.1014	+	49.8618i	0.438914	+	1.67043i
$892$	6.15435	−	10.6596i	0.206063	−	0.356911i
$893$	1.55694	+	0.566681i	0.0521011	+	0.0189633i
$894$	7.95806	+	27.4267i	0.266157	+	0.917285i
$895$	28.9812	−	10.5483i	0.968734	−	0.352590i
$896$	−5.21206	−	0.0267874i	−0.174123	−	0.000894903i
$897$	0.902380	−	13.5164i	0.0301296	−	0.451299i
$898$	−1.55222	−	8.80307i	−0.0517982	−	0.293762i
$899$	4.72093			0.157452
$900$	8.24971	+	4.32000i	0.274990	+	0.144000i
$901$	29.7677			0.991707
$902$	−98.5257	+	82.6729i	−3.28055	+	2.75271i
$903$	−27.8615	−	7.00556i	−0.927173	−	0.233130i
$904$	−0.742371	+	4.21020i	−0.0246909	+	0.140029i
$905$	−8.72364	+	3.17515i	−0.289984	+	0.105545i
$906$	56.2255	−	6.08867i	1.86797	−	0.202282i
$907$	−9.55243	−	54.1745i	−0.317183	−	1.79884i	−0.559707	−	0.828690i	$-0.689086\pi$
$907$	−9.55243	−	54.1745i	−0.317183	−	1.79884i	0.242524	−	0.970145i	$-0.422025\pi$
$908$	−53.5611			−1.77749
$909$	−6.29518	−	6.90354i	−0.208798	−	0.228976i
$910$	6.55853	+	38.3467i	0.217413	+	1.27118i
$911$	−19.5461	−	7.11419i	−0.647590	−	0.235704i	−0.00272069	−	0.999996i	$-0.500866\pi$
$911$	−19.5461	−	7.11419i	−0.647590	−	0.235704i	−0.644869	+	0.764293i	$0.723088\pi$
$912$	−0.239935	+	3.59388i	−0.00794503	+	0.119005i
$913$	13.6739	−	4.97691i	0.452541	−	0.164712i
$914$	14.6492	−	83.0795i	0.484551	−	2.74803i
$915$	15.6221	−	16.2794i	0.516449	−	0.538181i
$916$	7.58371	+	43.0094i	0.250573	+	1.42107i
$917$	5.47497	−	4.54630i	0.180800	−	0.150132i
$918$	24.3818	+	44.8283i	0.804720	+	1.47955i
$919$	−13.8544	−	23.9965i	−0.457014	−	0.791571i	0.541788	−	0.840515i	$-0.317748\pi$
$919$	−13.8544	−	23.9965i	−0.457014	−	0.791571i	−0.998802	+	0.0489442i	$0.984414\pi$
$920$	1.61794	+	0.588883i	0.0533420	+	0.0194149i
$921$	15.7007	+	54.1109i	0.517355	+	1.78301i
$922$	39.0426	+	32.7606i	1.28580	+	1.07891i
$923$	23.0531	+	19.3439i	0.758802	+	0.636711i
$924$	−32.6442	−	45.1194i	−1.07392	−	1.48432i
$925$	−11.2209	−	4.08408i	−0.368941	−	0.134284i
$926$	−23.5634	+	40.8129i	−0.774340	+	1.34120i
$927$	36.9824	+	4.96014i	1.21466	+	0.162912i
$928$	−3.82133	−	6.61873i	−0.125441	−	0.217271i
$929$	30.6315	+	11.1490i	1.00499	+	0.365785i	0.791506	−	0.611162i	$-0.209298\pi$
$929$	30.6315	+	11.1490i	1.00499	+	0.365785i	0.213481	+	0.976947i	$0.431520\pi$
$930$	18.0428	−	40.8709i	0.591648	−	1.34021i
$931$	3.00540	−	2.46963i	0.0984979	−	0.0809390i
$932$	10.6540	−	60.4217i	0.348983	−	1.97918i
$933$	−10.9179	+	1.18230i	−0.357436	+	0.0387069i
$934$	2.41235	+	13.6811i	0.0789344	+	0.447659i
$935$	−35.2232	−	61.0084i	−1.15192	−	1.99519i
$936$	−0.802187	−	1.95002i	−0.0262203	−	0.0637384i
$937$	14.2370	+	24.6593i	0.465104	+	0.805583i	0.999206	−	0.0398364i	$-0.0126837\pi$
$937$	14.2370	+	24.6593i	0.465104	+	0.805583i	−0.534102	+	0.845420i	$0.679350\pi$
$938$	9.14103	−	50.3274i	0.298465	−	1.64325i
$939$	−42.2383	+	20.7659i	−1.37839	+	0.677671i
$940$	−2.79244	+	15.8367i	−0.0910794	+	0.516537i
$941$	−6.88134	+	39.0260i	−0.224325	+	1.27221i	0.639645	+	0.768670i	$0.279081\pi$
$941$	−6.88134	+	39.0260i	−0.224325	+	1.27221i	−0.863971	+	0.503542i	$0.832030\pi$
$942$	−5.51267	−	18.9989i	−0.179613	−	0.619017i
$943$	−23.2581	+	19.5159i	−0.757389	+	0.635525i
$944$	−35.5342			−1.15654
$945$	−16.5411	−	30.7884i	−0.538083	−	1.00155i
$946$	−72.9052			−2.37035
$947$	5.14758	−	4.31933i	0.167274	−	0.140359i	−0.555308	−	0.831645i	$-0.687400\pi$
$947$	5.14758	−	4.31933i	0.167274	−	0.140359i	0.722582	+	0.691285i	$0.242955\pi$
$948$	−11.7666	−	2.89441i	−0.382162	−	0.0940061i
$949$	−0.225835	+	1.28078i	−0.00733092	+	0.0415757i
$950$	−0.286638	+	1.62560i	−0.00929976	+	0.0527415i
$951$	−5.60800	−	3.75700i	−0.181852	−	0.121829i
$952$	−2.40831	−	2.04200i	−0.0780539	−	0.0661815i
$953$	6.10269	+	10.5702i	0.197685	+	0.342401i	0.947778	−	0.318932i	$-0.103324\pi$
$953$	6.10269	+	10.5702i	0.197685	+	0.342401i	−0.750092	+	0.661333i	$0.769991\pi$
$954$	36.6096	−	8.02302i	1.18528	−	0.259755i
$955$	2.09440	+	3.62761i	0.0677732	+	0.117387i
$956$	5.10867	+	28.9727i	0.165226	+	0.937044i
$957$	3.78506	−	8.57397i	0.122354	−	0.277157i
$958$	2.90495	−	16.4748i	0.0938548	−	0.532277i
$959$	3.05783	−	5.23402i	0.0987426	−	0.169015i
$960$	−39.1408	+	4.23856i	−1.26326	+	0.136799i
$961$	5.66023	+	2.06015i	0.182588	+	0.0664566i
$962$	23.6014	+	40.8789i	0.760940	+	1.31799i
$963$	18.8993	−	11.9758i	0.609020	−	0.385914i
$964$	−8.59620	+	14.8891i	−0.276865	+	0.479544i
$965$	18.0076	+	6.55425i	0.579687	+	0.210989i
$966$	−14.9707	−	20.6918i	−0.481674	−	0.665749i
$967$	−7.93227	−	6.65596i	−0.255084	−	0.214041i	0.506274	−	0.862373i	$-0.331023\pi$
$967$	−7.93227	−	6.65596i	−0.255084	−	0.214041i	−0.761358	+	0.648332i	$0.775467\pi$
$968$	−4.12237	−	3.45908i	−0.132498	−	0.111179i
$969$	−3.22380	+	3.35945i	−0.103563	+	0.107921i
$970$	28.6386	+	10.4236i	0.919531	+	0.334682i
$971$	−18.0985	−	31.3475i	−0.580808	−	1.00599i	−0.995384	−	0.0959748i	$-0.969403\pi$
$971$	−18.0985	−	31.3475i	−0.580808	−	1.00599i	0.414575	−	0.910015i	$-0.363930\pi$
$972$	21.6542	+	24.9961i	0.694557	+	0.801750i
$973$	0.951954	+	5.56593i	0.0305183	+	0.178435i
$974$	−13.1471	−	74.5607i	−0.421259	−	2.38908i
$975$	2.01197	+	6.93406i	0.0644347	+	0.222068i
$976$	−3.32967	+	18.8835i	−0.106580	+	0.604446i
$977$	−39.0034	+	14.1961i	−1.24783	+	0.454173i	−0.879668	−	0.475589i	$-0.842235\pi$
$977$	−39.0034	+	14.1961i	−1.24783	+	0.454173i	−0.368162	+	0.929762i	$0.620013\pi$
$978$	2.28930	−	1.12551i	0.0732038	−	0.0359898i
$979$	−36.0450	−	13.1193i	−1.15200	−	0.419295i
$980$	28.6706	+	24.5641i	0.915848	+	0.784670i
$981$	−40.6330	−	21.2777i	−1.29731	−	0.679344i
$982$	−9.46086			−0.301908
$983$	−3.31834	−	18.8192i	−0.105838	−	0.600240i	−0.990882	−	0.134732i	$-0.956983\pi$
$983$	−3.31834	−	18.8192i	−0.105838	−	0.600240i	0.885044	−	0.465508i	$-0.154128\pi$
$984$	−1.90858	+	4.32335i	−0.0608434	+	0.137823i
$985$	−18.8205	+	6.85012i	−0.599672	+	0.218263i
$986$	1.61092	−	9.13600i	0.0513023	−	0.290950i
$987$	9.51082	−	9.80961i	0.302733	−	0.312243i
$988$	2.57296	−	2.15897i	0.0818567	−	0.0686859i
$989$	−17.2101			−0.547250
$990$	−59.7621	−	65.5374i	−1.89936	−	2.08292i
$991$	29.3668			0.932868			0.466434	−	0.884556i	$-0.345539\pi$
$991$	29.3668			0.932868			0.466434	+	0.884556i	$0.345539\pi$
$992$	7.02132	+	39.8199i	0.222927	+	1.26428i
$993$	40.1661	+	26.9087i	1.27463	+	0.853921i
$994$	56.7360	+	0.291594i	1.79956	+	0.00924881i
$995$	−2.35897	+	0.858594i	−0.0747843	+	0.0272193i
$996$	6.46313	−	6.73510i	0.204792	−	0.213410i
$997$	−33.7574	−	12.2867i	−1.06911	−	0.389124i	−0.253265	−	0.967397i	$-0.581505\pi$
$997$	−33.7574	−	12.2867i	−1.06911	−	0.389124i	−0.815843	+	0.578273i	$0.803727\pi$
$998$	−2.25194	+	3.90048i	−0.0712840	+	0.123467i
$999$	−31.7809	−	28.0764i	−1.00550	−	0.888299i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.u.a.67.4	✓	132
3.2	odd	2		567.2.u.a.172.19		132
7.2	even	3		189.2.w.a.121.19	yes	132
21.2	odd	6		567.2.w.a.415.4		132
27.2	odd	18		567.2.w.a.235.4		132
27.25	even	9		189.2.w.a.25.19	yes	132
189.2	odd	18		567.2.u.a.478.19		132
189.79	even	9	inner	189.2.u.a.79.4	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.67.4	✓	132	1.1	even	1	trivial
189.2.u.a.79.4	yes	132	189.79	even	9	inner
189.2.w.a.25.19	yes	132	27.25	even	9
189.2.w.a.121.19	yes	132	7.2	even	3
567.2.u.a.172.19		132	3.2	odd	2
567.2.u.a.478.19		132	189.2	odd	18
567.2.w.a.235.4		132	27.2	odd	18
567.2.w.a.415.4		132	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.55519 + 1.30496i) q^{2} +(1.19925 - 1.24972i) q^{3} +(0.368398 - 2.08929i) q^{4} +(0.441461 - 2.50365i) q^{5} +(-0.234236 + 3.50852i) q^{6} +(-0.472815 + 2.60316i) q^{7} +(0.123353 + 0.213653i) q^{8} +(-0.123586 - 2.99745i) q^{9} +O(q^{10})\)	\(q+(-1.55519 + 1.30496i) q^{2} +(1.19925 - 1.24972i) q^{3} +(0.368398 - 2.08929i) q^{4} +(0.441461 - 2.50365i) q^{5} +(-0.234236 + 3.50852i) q^{6} +(-0.472815 + 2.60316i) q^{7} +(0.123353 + 0.213653i) q^{8} +(-0.123586 - 2.99745i) q^{9} +(2.58060 + 4.46974i) q^{10} +(-0.994702 - 5.64123i) q^{11} +(-2.16922 - 2.96598i) q^{12} +(0.494719 - 2.80569i) q^{13} +(-2.66170 - 4.66541i) q^{14} +(-2.59943 - 3.55421i) q^{15} +(3.51651 + 1.27990i) q^{16} +(2.41871 + 4.18933i) q^{17} +(4.10375 + 4.50033i) q^{18} +(-0.277852 + 0.481253i) q^{19} +(-5.06822 - 1.84468i) q^{20} +(2.68619 + 3.71273i) q^{21} +(8.90852 + 7.47513i) q^{22} +(2.10296 + 1.76459i) q^{23} +(0.414937 + 0.102068i) q^{24} +(-1.37492 - 0.500430i) q^{25} +(2.89193 + 5.00897i) q^{26} +(-3.89418 - 3.44026i) q^{27} +(5.26457 + 1.94685i) q^{28} +(0.164033 + 0.930279i) q^{29} +(8.68070 + 2.13532i) q^{30} +(0.867833 - 4.92173i) q^{31} +(-7.60271 + 2.76716i) q^{32} +(-8.24285 - 5.52217i) q^{33} +(-9.22845 - 3.35888i) q^{34} +(6.30868 + 2.33296i) q^{35} +(-6.30808 - 0.846050i) q^{36} +8.16114 q^{37} +(-0.195903 - 1.11102i) q^{38} +(-2.91303 - 3.98299i) q^{39} +(0.589368 - 0.214513i) q^{40} +(-1.92050 + 10.8917i) q^{41} +(-9.02249 - 2.26863i) q^{42} +(-4.80243 + 4.02972i) q^{43} -12.1526 q^{44} +(-7.55914 - 1.01384i) q^{45} -5.57321 q^{46} +(-0.517743 - 2.93627i) q^{47} +(5.81670 - 2.85971i) q^{48} +(-6.55289 - 2.46163i) q^{49} +(2.79130 - 1.01595i) q^{50} +(8.13612 + 2.00136i) q^{51} +(-5.67965 - 2.06722i) q^{52} +(3.07682 - 5.32920i) q^{53} +(10.5456 + 0.268508i) q^{54} -14.5628 q^{55} +(-0.614496 + 0.220088i) q^{56} +(0.268216 + 0.924380i) q^{57} +(-1.46908 - 1.23270i) q^{58} +(-8.92291 + 3.24767i) q^{59} +(-8.38341 + 4.12160i) q^{60} +(0.889765 + 5.04611i) q^{61} +(5.07300 + 8.78669i) q^{62} +(7.86129 + 1.09553i) q^{63} +(4.47042 - 7.74299i) q^{64} +(-6.80608 - 2.47721i) q^{65} +(20.0254 - 2.16855i) q^{66} +(7.29506 + 6.12129i) q^{67} +(9.64378 - 3.51005i) q^{68} +(4.72722 - 0.511912i) q^{69} +(-12.8556 + 4.60437i) q^{70} +(-5.28149 + 9.14782i) q^{71} +(0.625171 - 0.396148i) q^{72} -0.456492 q^{73} +(-12.6921 + 10.6499i) q^{74} +(-2.27427 + 1.11812i) q^{75} +(0.903117 + 0.757805i) q^{76} +(15.1553 + 0.0778908i) q^{77} +(9.72794 + 2.39292i) q^{78} +(2.52613 - 2.11967i) q^{79} +(4.75684 - 8.23909i) q^{80} +(-8.96945 + 0.740884i) q^{81} +(-11.2265 - 19.4448i) q^{82} +(0.441119 + 2.50171i) q^{83} +(8.74656 - 4.24447i) q^{84} +(11.5564 - 4.20618i) q^{85} +(2.21007 - 12.5339i) q^{86} +(1.35930 + 0.910645i) q^{87} +(1.08257 - 0.908382i) q^{88} +(3.34817 - 5.79919i) q^{89} +(13.0789 - 8.28763i) q^{90} +(7.06976 + 2.61441i) q^{91} +(4.46147 - 3.74362i) q^{92} +(-5.11001 - 6.98694i) q^{93} +(4.63689 + 3.89081i) q^{94} +(1.08223 + 0.908098i) q^{95} +(-5.65940 + 12.8198i) q^{96} +(4.52344 - 3.79562i) q^{97} +(13.4033 - 4.72295i) q^{98} +(-16.7864 + 3.67875i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9} + 3 q^{10} - 15 q^{11} - 3 q^{12} - 12 q^{13} - 30 q^{14} + 9 q^{16} + 27 q^{17} - 3 q^{18} + 3 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} - 36 q^{23} - 72 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 3 q^{30} - 3 q^{31} - 75 q^{32} + 15 q^{33} - 18 q^{34} + 15 q^{35} - 60 q^{36} - 6 q^{37} + 69 q^{38} + 51 q^{39} + 51 q^{40} - 39 q^{42} - 12 q^{43} - 6 q^{44} - 21 q^{45} - 6 q^{46} - 21 q^{47} + 90 q^{48} - 42 q^{49} - 39 q^{50} + 33 q^{51} + 9 q^{52} + 9 q^{53} - 9 q^{54} - 24 q^{55} + 111 q^{56} - 18 q^{57} - 3 q^{58} + 27 q^{59} - 63 q^{60} - 21 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} - 90 q^{65} - 3 q^{66} - 3 q^{67} - 30 q^{68} - 6 q^{69} + 39 q^{70} - 18 q^{71} + 183 q^{72} - 42 q^{73} + 51 q^{74} - 45 q^{75} - 24 q^{76} + 15 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} - 87 q^{81} - 6 q^{82} - 42 q^{83} + 135 q^{84} - 63 q^{85} - 93 q^{86} + 75 q^{87} - 51 q^{88} + 75 q^{89} - 39 q^{90} - 21 q^{91} - 66 q^{92} + 81 q^{93} + 33 q^{94} + 15 q^{95} - 171 q^{96} - 12 q^{97} - 36 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9 + 3 * q^10 - 15 * q^11 - 3 * q^12 - 12 * q^13 - 30 * q^14 + 9 * q^16 + 27 * q^17 - 3 * q^18 + 3 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 - 36 * q^23 - 72 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 3 * q^30 - 3 * q^31 - 75 * q^32 + 15 * q^33 - 18 * q^34 + 15 * q^35 - 60 * q^36 - 6 * q^37 + 69 * q^38 + 51 * q^39 + 51 * q^40 - 39 * q^42 - 12 * q^43 - 6 * q^44 - 21 * q^45 - 6 * q^46 - 21 * q^47 + 90 * q^48 - 42 * q^49 - 39 * q^50 + 33 * q^51 + 9 * q^52 + 9 * q^53 - 9 * q^54 - 24 * q^55 + 111 * q^56 - 18 * q^57 - 3 * q^58 + 27 * q^59 - 63 * q^60 - 21 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 - 90 * q^65 - 3 * q^66 - 3 * q^67 - 30 * q^68 - 6 * q^69 + 39 * q^70 - 18 * q^71 + 183 * q^72 - 42 * q^73 + 51 * q^74 - 45 * q^75 - 24 * q^76 + 15 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 - 87 * q^81 - 6 * q^82 - 42 * q^83 + 135 * q^84 - 63 * q^85 - 93 * q^86 + 75 * q^87 - 51 * q^88 + 75 * q^89 - 39 * q^90 - 21 * q^91 - 66 * q^92 + 81 * q^93 + 33 * q^94 + 15 * q^95 - 171 * q^96 - 12 * q^97 - 36 * q^98 + 24 * q^99

Introduction

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